Question

The graph of the polynomial f(x) = ax² + bx + c is as shown in figure. Write the value of b² – 4ac and the number of real zeros of f(x).

Answer 1

The graph of the polynomial f(x) = ax² + bx + c or the curve touches x-axis at point `((-b)/2a, 0)`. The x-coordinate of this point gives two equal zeros of the polynomial and b² – 4ac = 0.

Hence the number of real zeros of  f(x) is 2 and b² – 4ac = 0.