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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.

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Solution

Let f(x) = ax2 + bx + c

If f(x) has two real and distinct zeroes, the parabola represented by f(x) cuts x-axis at two distinct points.

If f(x) has two real and equal zeroes, the parabola represented by f(x) touches x-axis at only one distinct point.

Hence, if the parabola represented by f(x) = ax2 + bx + c cuts x-axis at two distinct points, then the polynomial ax2 + bx + c has 2 real zeroes.

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