Figure 2.23 shows the graph of the polynomial f(x) = ax^{2} + bx + c for which

As seen from the graph,

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

One root is positive & one root is negative.

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

α + β = -b/a

Also, the product of roots = c/a is positive.

Because c is positive,

⇒ a is negative & b is negative.

Therefore, option (b) is correct.

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