Question

which function has real zeros at x = 3 and x = 7?
a) ( f(x) = x^2 + 4x - 21 )
b) ( f(x) = x^2 - 4x - 21 )
c) ( f(x) = x^2 - 10x + 21 )
d) ( f(x) = x^2 - 10x - 21 )

Explanation:

Step1: Form factor from zeros

If $x=3$ and $x=7$ are zeros, then $(x-3)$ and $(x-7)$ are factors.

Step2: Multiply factors to get polynomial

$$f(x)=(x-3)(x-7)$$
Expand the product:
$$f(x)=x^2 -7x -3x +21$$

Step3: Combine like terms

$$f(x)=x^2 -10x +21$$

Answer:

$\boldsymbol{f(x) = x^2 - 10x + 21}$ (the second option)