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Figure 2.23 shows the graph of the polynomial f(x) = ax2 + 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.