10th Class Mathematics Polynomials Question Bank

done Assertion And Reason (MCQs) - Polynomials Total Questions - 19

• question_answer1)

  Directions (Q. Nos. 1 - 19): In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

  Assertion (A): \[9{{x}^{4}}+8{{x}^{3}}+4x+1\] is a biquadratic polynomial.

  Reason (R): A polynomial of degree 4 is a biquadratic polynomial.

   
  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer2)

  Assertion (A): \[f(x)=2{{x}^{3}}-\frac{3}{x}+7\] is a polynomial in the variable x of degree 3.

  Reason (R): The highest power of x in a polynomial \[f(x)\] is called the degree of the polynomial \[f(x)\].

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer3)

  Assertion (A): The graph of the polynomial \[f(x)={{x}^{3}}-4x,\] cuts the X-axis at 3 different points.

  Reason (R): The graph of a cubic polynomial always cross X-axis at least once and at most thrice.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer4)

  Assertion (A): The polynomial \[p(x)={{x}^{3}}+x\] has one real zero.

  Reason (R): A polynomial of nth degree has at most n zeroes.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer5)

  Assertion (A): If one zero of the polynomial \[p(x)=({{k}^{2}}+9){{x}^{2}}+9x+6k\] is the reciprocal of the other zero, then \[\text{k}=\text{3}\].

  Reason (R): If \[(x-\alpha )\] is a factor of the polynomial \[p(x),\]then a is a zero of \[p(x)\].

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer6)

  Assertion (A): A monic quadratic polynomial having 5 and \[-3\] as zeroes is \[{{\text{x}}^{\text{2}}}-\text{2x}-\text{15}\].

  Reason (R): The monic quadratic polynomial having a and (3 as zeroes is given by \[p(x)={{x}^{2}}-(\alpha +\beta )x+\alpha \beta \].

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer7)

  Assertion (A): If two zeroes of the polynomial \[f(x)={{x}^{3}}-2{{x}^{2}}-3x+6\] are \[\sqrt{3}\] and \[-\sqrt{3},\] then its third zero is 4.

  Reason (R): If \[\alpha ,\beta \] and \[\gamma \] be the zeroes of the polynomial \[f(x)=a{{x}^{3}}+b{{x}^{2}}+cx+d\]. Then,

  Sum of the zeroes \[=-\frac{Coefficient\,\,of\,\,{{x}^{2}}}{Coefficient\,\,of\,\,{{x}^{2}}}\]

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer8)

  Assertion (A): If the sum and product of zeroes of a quadratic polynomial is 3 and \[-2\] respectively, then the quadratic polynomial is\[{{x}^{2}}-3x-2\]

  Reason (R): If S is the sum of zeroes and P is the product of zeroes of a quadratic polynomial then the quadratic polynomial is given by \[{{x}^{2}}-Sx+P\].

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer9)

  Assertion (A): If \[\alpha ,\beta ,\gamma \] are the zeroes of \[{{x}^{3}}-2{{x}^{2}}+qx-r\]and \[\alpha +\beta =0,\] then \[2q=r\].

  Reason (R): If a, p, y are the zeroes of \[a{{x}^{3}}+b{{x}^{2}}+cx+d,\]then

  \[\alpha +\beta +\gamma =-\frac{b}{a}\]

  \[\alpha \beta +\beta \gamma +\gamma \alpha =\frac{c}{a}\]

  \[\alpha \beta \gamma =-\frac{d}{a}\]

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer10)

  Assertion (A): \[(2-\sqrt{3})\] is one zero of the quadratic polynomial then other zero will be \[(2+\sqrt{3})\].

  Reason (R): Irrational zeroes (roots) always occurs in pairs.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer11)

  Assertion (A): Zeroes of \[f(x)={{x}^{2}}-4x-5\] are \[5,-1\].

  Reason (R): The polynomial whose zeroes are \[2+\sqrt{3},\] \[2-\sqrt{3}\]is \[{{x}^{2}}-4x+7\]

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer12)

  Assertion (A): \[{{x}^{2}}+4x+5\] has two zeroes.

  Reason (R): A quadratic polynomial can have at the most two zeroes.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer13)

  Assertion   (A):   If   one   zero   of   polynomial\[p(x)=({{k}^{2}}+4){{x}^{2}}+13x+4k\]is reciprocal of other, then \[k=2\].

  Reason (R): If \[(x-\alpha )\] is a factor of \[p(x),\] then \[p(\alpha )=0\]i.e., \[\alpha \]is a zero of \[p(x)\].

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer14)

  Assertion (A): \[P(x)=14{{x}^{3}}-2{{x}^{2}}+8{{x}^{4}}+7x-8\]is polynomial of degree 3.

  Reason (R): The highest power of x in the polynomial \[p(x)\]is the degree of the polynomial.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer15)

  Assertion (A): \[{{x}^{3}}+x\] has only one real zero.

  Reason (R): A polynomial of nth degree must have n real zeroes.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer16)

  Assertion (A): The sum and product of the zeroes of a quadratic polynomial are \[-\frac{1}{4}\] and \[\frac{1}{4}\] respectively.

  Then the quadratic polynomial is \[4{{x}^{2}}+x+1\].

  Reason (R): The quadratic polynomial whose sum a product of zeroes are given is \[{{x}^{2}}-\] (sum of zeroes) \[x+\]product of zeroes).

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer17)

  Assertion (A): If both zeroes of the quadratic polynomial \[{{x}^{2}}-2kx+2\]are equal in magnitude but opposite in sign then value of k is -.

  Reason (R): Sum of zeroes of a quadratic polynomial \[a{{x}^{2}}+bx+c\] is \[\frac{-b}{a}\].

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer18)

  Assertion (A): Degree of a zero polynomial is not defined.

  Reason (R): Degree of a non-zero constant polynomial is '0'.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer19)

  Assertion (A): The graph \[y=f(x)\] is shown in figure, for the polynomia \[f(x)\]. The number of zeroes of \[f(x)\] is 4.

  Reason (R): The number of zeroes of the polynomial \[f(x)\]is the number of points of which \[f(x)\] cuts or touches the axes.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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