Question

What are the zeros of f(x) = x^2 + x - 20?
0 x=-5 and x=4
0 x= -4 and x = 5
0 x= -2 and x = 10
0x= -10 and x = 2

Answer 1

To find the zeros of the quadratic function \( f(x) = x^2 + x - 20 \), we need to solve the equation \( f(x) = 0 \). This means we solve:

\[
x^2 + x - 20 = 0
\]

We can factor the quadratic expression:

Looking for two numbers that multiply to \(-20\) and add to \(1\) (the coefficient of \(x\)), we find:

\[
5 \text{ and } -4
\]

Thus, the factorization is:

\[
(x + 5)(x - 4) = 0
\]

Setting each factor equal to zero gives us:

1. \(x + 5 = 0 \implies x = -5\)
2. \(x - 4 = 0 \implies x = 4\)

So the zeros of the function \( f(x) = x^2 + x - 20 \) are:

\[
x = -5 \quad \text{and} \quad x = 4
\]

The correct answer is:

0 \( x = -5 \) and \( x = 4 \)