Question

which function has zeros at x = -2 and x = 5?
○ f(x) = x² + 2x - 10
○ f(x) = x² - 2x - 10
○ f(x) = x² + 3x - 10
○ f(x) = x² - 3x - 10

Explanation:

Step1: Recall the factor theorem

If a function \( f(x) \) has a zero at \( x = a \), then \( (x - a) \) is a factor of \( f(x) \). So for zeros at \( x=-2 \) and \( x = 5 \), the factors are \( (x + 2) \) and \( (x - 5) \).

Step2: Multiply the factors

To find the quadratic function, we multiply the two factors:

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Answer:

\( f(x)=x^2 - 3x - 10 \) (the fourth option: \( f(x)=x^2 - 3x - 10 \))