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