10th Class Mathematics Polynomials Question Bank

done Case Based (MCQs) - Polynomials Total Questions - 40

• question_answer1)

  Case Study - 1 : Q. 1 to 5

  The below pictures show few natural examples of parabolic shape which can be represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms. Based on the above information, answer the following questions:

  In the standard form of quadratic polynomial, \[a{{x}^{2}}+bx+c,\] a, b and c:
  A)
  all are real numbers done clear
  B)
  all are rational numbers done clear
  C)
  'a' is a non-zero real number and b and c are any real numbers done clear
  D)
  all are integers done clear
  View Solution play_arrow

• question_answer2)
  If the roots of the quadratic polynomial are equal, and the discriminant \[D={{b}^{2}}-4ac,\] then:
  A)
  \[D>0\] done clear
  B)
  \[D<0\]      done clear
  C)
  \[D\ge 0\] done clear
  D)
  \[D=0\] done clear
  View Solution play_arrow

• question_answer3)
  If \[\alpha \] and \[\frac{1}{\alpha }\]are the zeroes of the quadratic polynomial \[2{{x}^{2}}-x+8k,\] then k is:
  A)
  \[4\] done clear
  B)
  \[\frac{1}{4}\] done clear
  C)
  \[\frac{-1}{4}\] done clear
  D)
  \[2\] done clear
  View Solution play_arrow

• question_answer4)
  The graph of \[{{\text{x}}^{\text{2}}}+\text{4}=0:\]
  A)
  intersects X-axis at two distinct points done clear
  B)
  touches X-axis at a point done clear
  C)
  neither touches nor intersects X-axis done clear
  D)
  either touches or intersects X-axis. done clear
  View Solution play_arrow

• question_answer5)
  If the sum of the roots is \[-p\] and product of the roots \[-\frac{1}{p}\] is, then the quadratic polynomial is:
  A)
  \[k\left( -p{{x}^{2}}+\frac{x}{p}+1 \right)\] done clear
  B)
  \[k\left( p{{x}^{2}}-\frac{x}{p}-1 \right)\] done clear
  C)
  \[k\left( {{x}^{2}}+px-\frac{1}{p} \right)\] done clear
  D)
  \[k\left( {{x}^{2}}-px+\frac{1}{p} \right)\] done clear
  View Solution play_arrow

• question_answer6)

  Case Study : Q. 6 to 10

  Manya is a body posture, originally and still a general term for a sitting meditation pose, and later extended in hatha yoga and modem yoga as exercise, to any type of pose or position, adding reclining, standing, inverted, twisting, and balancing poses. In the figure, one can observe that poses can be related to representation of quadratic polynomial.

  Based on the above information, answer the following questions:

  The shape of the poses shown is:
  A)
  spiral done clear
  B)
  ellipse done clear
  C)
  linear done clear
  D)
  parabola done clear
  View Solution play_arrow

• question_answer7)
  The graph of parabola opens downwards, if..........
  A)
  \[a\ge 0\] done clear
  B)
  \[a=0\] done clear
  C)
  \[a<0\] done clear
  D)
  \[a>0\] done clear
  View Solution play_arrow

• question_answer8)

  In the graph, how many zeroes are there for the polynomial?

  A)
  0 done clear
  B)
  1 done clear
  C)
  2 done clear
  D)
  3 done clear
  View Solution play_arrow

• question_answer9)
  The quadratic polynomial of the two zeroes in the above shown graph are:
  A)
  \[k({{x}^{2}}-2x-8)\] done clear
  B)
  \[k({{x}^{2}}+2x-8)\] done clear
  C)
  \[k({{x}^{2}}+2x+8)\] done clear
  D)
  \[k({{x}^{2}}-2x+8)\] done clear
  View Solution play_arrow

• question_answer10)
  The   zeroes   of   the   quadratic   polynomial \[4\sqrt{3}\,{{x}^{2}}+5x-2\sqrt{3}\] are:
  A)
  \[\frac{2}{\sqrt{3}}.\frac{\sqrt{3}}{4}\] done clear
  B)
  \[-\frac{2}{\sqrt{3}}.\frac{\sqrt{3}}{4}\] done clear
  C)
  \[\frac{2}{\sqrt{3}}.-\frac{\sqrt{3}}{4}\] done clear
  D)
  \[-\frac{2}{\sqrt{3}}.-\frac{\sqrt{3}}{4}\] done clear
  View Solution play_arrow

• question_answer11)

  Case Study : Q. 11 to 15
  Applications   of   parabolas - highway   overpasses/ underpasses. A highway underpass is parabolic in shape.
  Parabola: A parabola is the graph that results from \[p(x)=a{{x}^{2}}+bx+c\] Parabolas are symmetric about a vertical line known as the axis of symmetry.
  Parabolic chamber \[y=2{{x}^{2}}/nw\]
  The axis of symmetry runs through the maximum or minimum point of the parabola which is called the vertex.
  Based on the above information, answer the following questions.
  If the highway overpass is represented by \[{{x}^{2}}-2x-8\].
  Then its zeroes are:

  A)
  \[(2,-4)\] done clear
  B)
  \[(4,-2)\] done clear
  C)
  \[(-2,-2)\] done clear
  D)
  \[(-4,-4)\] done clear
  View Solution play_arrow

• question_answer12)

  The highway overpass is represented graphically.

  Zeroes of a polynomial can be expressed graphically.

  Number of zeroes of polynomial is equal to number of points where the graph of polynomial:

  A)
  Intersects X-axis done clear
  B)
  Intersects V-axis done clear
  C)
  Intersects /-axis or X-axis done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer13)
  Graph of a quadratic polynomial is a:
  A)
  straight line done clear
  B)
  circle done clear
  C)
  parabola done clear
  D)
  ellipse done clear
  View Solution play_arrow

• question_answer14)
  The representation of Highway Underpass whose one zero is 6 and sum of the zeroes is 0, is:
  A)
  \[{{x}^{2}}-6x+2\] done clear
  B)
  \[{{x}^{2}}-36\] done clear
  C)
  \[{{x}^{2}}-6\] done clear
  D)
  \[{{x}^{2}}-3\] done clear
  View Solution play_arrow

• question_answer15)
  The number of zeroes that polynomial \[f(x)={{(x-2)}^{2}}+4\] can have is:
  A)
  1 done clear
  B)
  2 done clear
  C)
  0 done clear
  D)
  3 done clear
  View Solution play_arrow

• question_answer16)

  Case Study : Q. 16 to 20

  A student was given the task to prepare a graph of quadratic polynomial \[y=-8-2x+{{x}^{2}}.\]. To draw this graph he take seven values of y corresponding to different values of x. After plotting the points on the graph paper with suitable scale, he obtain the graph as shown below.

  Based on the above graph, answer the following questions:

  What is the graph of a quadratic polynomial called?
  A)
  Parabola done clear
  B)
  Hyperbola done clear
  C)
  Ellipse done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer17)
  The zeroes of given quadratic polynomial are:
  A)
  \[2,-4\] done clear
  B)
  \[-2,4\] done clear
  C)
  \[3,-4\] done clear
  D)
  \[-3,4\] done clear
  View Solution play_arrow

• question_answer18)
  Read from the graph the value of y corresponding to \[x=-1\] is:
  A)
  \[-8\] done clear
  B)
  \[-6\] done clear
  C)
  \[-5\] done clear
  D)
  \[-2\] done clear
  View Solution play_arrow

• question_answer19)
  The graph of the given quadratic polynomial cut at which points on the X-axis?
  A)
  \[(-2,0),\,\,(4,0)\] done clear
  B)
  \[(0,-2),\,\,(0,4)\] done clear
  C)
  \[(0,-2),\,\,(0,-8)\] done clear
  D)
  \[None\,\, of\,\, the\,\,above\] done clear
  View Solution play_arrow

• question_answer20)
  The graph of the given quadratic polynomial cut at which point on X-axis?
  A)
  \[(-8,0)\] done clear
  B)
  \[(0,-8)\] done clear
  C)
  \[(-10,0)\] done clear
  D)
  \[(-10,0)\] done clear
  View Solution play_arrow

• question_answer21)

  Case Study : Q. 21 to 25

  In a classroom, four students Anil, Jay, Richa and Suresh were asked to draw the graph of \[p(x)=a{{x}^{2}}+bx+c\].

  Following graphs are drawn by the students:

  Based on the above graphs, answer the following questions:

  How many students have drawn the graph correctly?
  A)
  1 done clear
  B)
  2 done clear
  C)
  3 done clear
  D)
  4 done clear
  View Solution play_arrow

• question_answer22)
  Which type of polynomial is represented by Jay's graph?
  A)
  Linear done clear
  B)
  Parabola done clear
  C)
  Zig-zag done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer23)
  How many zeroes are there for the Richa's graph?
  A)
  1 done clear
  B)
  2 done clear
  C)
  3 done clear
  D)
  4 done clear
  View Solution play_arrow

• question_answer24)
  If \[p(x)=a{{x}^{2}}+bx+c\] and \[a+b+c=0,\] then one zero is:
  A)
  \[\frac{-b}{a}\]  done clear
  B)
  \[\frac{c}{a}\] done clear
  C)
  \[\frac{b}{c}\] done clear
  D)
  \[-\frac{c}{a}\] done clear
  View Solution play_arrow

• question_answer25)
  If \[p(x)=a{{x}^{2}}+bx+c\] and \[a+c=b,\] then one of the zeroes is:
  A)
  \[\frac{b}{a}\] done clear
  B)
  \[\frac{c}{a}\] done clear
  C)
  \[\frac{-c}{a}\] done clear
  D)
  \[\frac{-b}{a}\] done clear
  View Solution play_arrow

• question_answer26)

  Case Study : Q. 26 to 30

  Ramesh was asked by one of his friends to find the polynomial whose zeroes are \[\frac{-2}{\sqrt{3}}\] and \[\frac{\sqrt{3}}{4}\]. He obtained the polynomial as shown below:

  Let \[\alpha =\frac{-2}{\sqrt{3}}\] and \[\alpha =\frac{\sqrt{3}}{4}\]

  \[\Rightarrow \,\,\,\,\,\,\,\alpha +\beta =\frac{-2}{\sqrt{3}}+\frac{\sqrt{3}}{4}=\frac{-8+1}{4\sqrt{3}}=\frac{-7}{4\sqrt{3}}\]

  \[\Rightarrow \,\,\,\,\,\,\,\alpha \beta =\frac{-2}{\sqrt{3}}\times \frac{\sqrt{3}}{4}=\frac{-1}{2}\]

  Required polynomial \[={{x}^{2}}-(\alpha +\beta )x+\alpha \beta \]

  \[={{x}^{2}}-\left( \frac{-7}{4\sqrt{3}} \right)x+\left( \frac{-1}{2} \right)\]

  \[={{x}^{2}}+\frac{7x}{4\sqrt{3}}-\frac{1}{2}\]

  \[=4\sqrt{3}{{x}^{2}}+7x-2\sqrt{3}\]

  His another friend Kavita pointed out that the polynomial obtained is not correct.

  Based on the above situation, answer the following questions:

  Is the claim of Kavita correct?
  A)
  Yes done clear
  B)
  No done clear
  C)
  Can't say done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer27)
  If yes, then the correct quadratic polynomial is:
  A)
  \[4\sqrt{3}{{x}^{2}}-5x+2\sqrt{3}\] done clear
  B)
         \[4\sqrt{3}{{x}^{2}}+5x-2\sqrt{3}\] done clear
  C)
  \[4\sqrt{3}{{x}^{2}}+5x+2\sqrt{3}\] done clear
  D)
  \[4\sqrt{3}{{x}^{2}}-5x-2\sqrt{3}\] done clear
  View Solution play_arrow

• question_answer28)
  The value of \[{{\alpha }^{2}}+{{\beta }^{2}}\] is:
  A)
  \[\frac{53}{48}\] done clear
  B)
  \[\frac{59}{48}\] done clear
  C)
  \[\frac{73}{48}\] done clear
  D)
  \[\frac{71}{48}\] done clear
  View Solution play_arrow

• question_answer29)
  What is the value of the correct polynomial if \[x=-1\]?
  A)
  \[-5+2\sqrt{3}\] done clear
  B)
  \[5-2\sqrt{3}\] done clear
  C)
  \[5-6\sqrt{3}\] done clear
  D)
  \[-5+6\sqrt{3}\] done clear
  View Solution play_arrow

• question_answer30)
  The value of \[{{\alpha }^{3}}-{{\beta }^{3}}\]is:
  A)
  \[\frac{-539}{192\sqrt{3}}\] done clear
  B)
  \[\frac{539}{192\sqrt{3}}\] done clear
  C)
  \[\frac{539\sqrt{3}}{192}\] done clear
  D)
  \[\frac{-539\sqrt{3}}{192}\] done clear
  View Solution play_arrow

• question_answer31)

  Case Study : Q. 31 to 35

  A group of school friends went on an expedition to see caves. One person remarked that the entrance of the caves resembles a parabola, and can be represented by a quadratic polynomial \[f(x)=a{{x}^{2}}+bx+c,\] \[a\ne 0,\] where a, b and c are real numbers.

  Based on the above information give the answer of the following questions.

  If one of the zeroes of the quadratic polynomial \[(p-1){{x}^{2}}+px+1\]is 4, then the value of p is:
  A)
  \[\frac{3}{5}\] done clear
  B)
  \[\frac{3}{4}\] done clear
  C)
  \[\frac{2}{5}\] done clear
  D)
  \[\frac{1}{5}\] done clear
  View Solution play_arrow

• question_answer32)
  The zeroes of the quadratic polynomial \[{{x}^{2}}+20x+96\]are:
  A)
  both positive done clear
  B)
  both negative done clear
  C)
  one positive and other negative done clear
  D)
  both equal done clear
  View Solution play_arrow

• question_answer33)
  The quadratic polynomial whose zeroes are 5 and \[-12\] is given by:
  A)
  \[{{x}^{2}}+7x-60\] done clear
  B)
  \[15{{x}^{2}}-x-6\] done clear
  C)
  \[{{x}^{2}}-7x+60\] done clear
  D)
  \[15{{x}^{2}}+x+6\] done clear
  View Solution play_arrow

• question_answer34)
  If one zero of the polynomial \[f(x)=5{{x}^{2}}+13x+m\] is reciprocal of the other, then the value of m is:
  A)
  6 done clear
  B)
  0 done clear
  C)
  5 done clear
  D)
  1 done clear
  View Solution play_arrow

• question_answer35)
  Which of the following cannot be the graph, of a quadratic polynomial?
  A)
  done clear
  B)
  done clear
  C)
  done clear
  D)
  done clear
  View Solution play_arrow

• question_answer36)

  Case Study : Q. 36 to 40

  Naveeka everyday goes to swimming. One day, Naveeka noticed the water coming out of the pipes to fill the pool.

  She then told her brother that the shape of the path of the water falling is like that of a parabola and also that a parabola can be represented by a quadratic polynomial which has atmost two zeroes.

  Based on the given information, answer the following questions.

  The number of zeroes that polynomial \[f(x)={{(x+2)}^{2}}+6\]can have is:
  A)
  0 done clear
  B)
  1 done clear
  C)
  2 done clear
  D)
  3 done clear
  View Solution play_arrow

• question_answer37)
  If the product of the zeroes of the quadratic polynomial \[f(x)=a{{x}^{2}}-6x-6\] is 4, then the value of a is:
  A)
  \[\frac{-3}{2}\] done clear
  B)
  \[\frac{3}{2}\] done clear
  C)
  \[\frac{2}{3}\] done clear
  D)
  \[\frac{-2}{3}\] done clear
  View Solution play_arrow

• question_answer38)
  The flow of the water in the pool is represented by \[{{x}^{2}}-2x-8,\] then its zeroes are:
  A)
  \[2,-4\] done clear
  B)
  \[4,-2\] done clear
  C)
  \[2,-2\] done clear
  D)
  \[-4,-4\] done clear
  View Solution play_arrow

• question_answer39)
  If a and p be the zeroes of the polynomial \[{{x}^{2}}-1,\]then the value of \[\frac{1}{\alpha }+\frac{1}{\beta }\]is:
  A)
  \[0\] done clear
  B)
  \[\frac{1}{2}\] done clear
  C)
  \[1\] done clear
  D)
  \[-1\] done clear
  View Solution play_arrow

• question_answer40)
  A quadratic polynomial whose one zero is \[-3\] and product of zeroes is 0, is:
  A)
  \[3{{x}^{2}}+3\] done clear
  B)
  \[{{x}^{2}}-3x\] done clear
  C)
  \[{{x}^{2}}+3x\] done clear
  D)
  \[3{{x}^{2}}-3\] done clear
  View Solution play_arrow