Q. 9

If the diagram in Fig. 2.22 shows the graph of the polynomial f (x) = ax2 + bx + c, then


A. a > 0, b<0 andc > 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

Answer :

As seen from the graph,


The parabola cuts the graph at two points on the positive x-axis.


Hence, both the roots are positive.


Now, for a polynomial, the sum of roots is given as:


α + β = -b/a


the sum will be positive as the roots are positive.


Also, the product of roots = c/a has to be positive too.


a is positive.


Now, since a is positive, therefore for the sum of roots to be negative, b has to be negative.


a > 0, b< 0 & c > 0.


Therefore, option (a) is correct.

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