Question

If the diagram in Fig. shows the graph of the polynomial

f (x) = ax² + 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

Answer 1

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.