Question

which function has real zeros at x = 3 and x = 7?
f(x) = x² + 4x - 21
f(x) = x² - 4x - 21
f(x) = x² - 10x + 21
f(x) = x² - 10x - 21

Explanation:

Step1: Recall the factored form of a quadratic function

If a quadratic function has real zeros at \( x = a \) and \( x = b \), then its factored form is \( f(x)=(x - a)(x - b) \). Here, \( a = 3 \) and \( b = 7 \), so the factored form is \( f(x)=(x - 3)(x - 7) \).

Step2: Expand the factored form

Using the distributive property (FOIL method):

$$
LATEXBLOCK0
$$

Answer:

\( f(x)=x^{2}-10x + 21 \) (the third option: \( f(x) = x^2 - 10x + 21 \))