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Question
The graph of the polynomial f(x) = ax2 + bx + c is as shown below (Fig. 2.19). Write the signs of 'a' and b2 − 4ac.
Solution
Clearly, `f(x) = ax^2 bx + c` represent a parabola opening upwards. Therefore, `a > 0`
Since the parabola cuts x-axis at two points, this means that the polynomial will have two real solutions
Hence `b^2 - 4 ac > 0`
Hence ` a> 0 `and `b^2 - 4ac > 0 `
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