10th Class Mathematics Polynomials Question Bank MCQs - Polynomials

The given figure shows the graph of the polynomial \[f(x)=a{{x}^{2}}+bx+c,\] then:

A) \[a>0,\,\,b<0\] and \[c>0\]

B) \[a<0,\,\,b<0\] and \[c>0\]

C) \[a<0,\,\,\,b>0\]and \[c>0\]

D) \[a<0,\,\,b>0\]and \[c<0\]

Correct Answer: B

Solution :

[b] Since \[y=a{{x}^{2}}+bx+c\]represents a parabola opening downward, so \[a<0\].

Also, vertex \[\left( -\frac{b}{2a},-\frac{D}{4a} \right)\]of the parabola lies in second quadrant.

\[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,-\frac{b}{2a}<0\Rightarrow b<0\] \[(a<0)\]

Now, \[y=a{{x}^{2}}+bx+c\] cuts V-axis at P. On putting \[x=0\]in \[y=a{{x}^{2}}+bx+c,\] we get\[y=c\]. So, coordinates of P are \[(0,c)\] which lies on positive direction of V-axis.

\[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,c>0\]

Hence, \[a<0,\,b<0\]and \[c>0\].

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10th Class Mathematics Polynomials Question Bank MCQs - Polynomials

question_answer The given figure shows the graph of the polynomial \[f(x)=a{{x}^{2}}+bx+c,\] then: A) \[a>0,\,\,b<0\] and \[c>0\] B) \[a<0,\,\,b<0\] and \[c>0\] C) \[a<0,\,\,\,b>0\]and \[c>0\] D) \[a<0,\,\,b>0\]and \[c<0\]

The given figure shows the graph of the polynomial \[f(x)=a{{x}^{2}}+bx+c,\] then:

A) \[a>0,\,\,b<0\] and \[c>0\]

B) \[a<0,\,\,b<0\] and \[c>0\]

C) \[a<0,\,\,\,b>0\]and \[c>0\]

D) \[a<0,\,\,b>0\]and \[c<0\]