Question

A function below, f(x), has factors (x - 5) and (x + 31), f(x) =x$ - 15x^ + 80x3 - 240x? + 639×— 945 What is the total number of real zeros of f(x)?

Answer 1

Hello,

f(x) = (x - 5)(x + 31)(x^2 - 15x + 21)

The quadratic factor x^2 - 15x + 21 has no real roots because its discriminant is negative. Therefore, the total number of real zeros of f(x) is equal to the number of real roots of the factors (x - 5) and (x + 31), which is 1 each. Hence the total number of real zeros of f(x) is 2.

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