Question

If the parabola represented by f(x) = ax² + bx + c cuts x-axis at two distinct points, then the polynomial ax² + bx + c has ______ real zeroes.

Answer 1

If the parabola represented by f(x) = ax² + bx + c cuts x-axis at two distinct points, then the polynomial ax² + bx + c has two real zeroes.

Explanation:

The x-coordinates of the two distinct x-intercepts are the two zeros of ax² + bx + c, so the polynomial has two distinct real roots. Equivalently, this happens when the discriminant D = b² – 4ac is positive (D > 0).