Question

what are the zeros of f(x)=x^2+x-20

x=-5 and x=4
x=-4 and x=5
x=-10 and x=2
x=-2 and x=10

Answer 1

To find the zeros of the function \( f(x) = x^2 + x - 20 \), we can solve the equation \( f(x) = 0 \).

This leads to:

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

To factor this quadratic equation, we look for two numbers that multiply to \(-20\) (the constant term) and add up to \(1\) (the coefficient of \(x\)).

The numbers \(5\) and \(-4\) fit this requirement since:

\[
5 \times (-4) = -20 \quad \text{and} \quad 5 + (-4) = 1
\]

Thus, we can factor the equation as:

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

Setting each factor equal to zero gives us the zeros:

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

So, the zeros of \( f(x) = x^2 + x - 20 \) are \( x = -5 \) and \( x = 4 \).

Therefore, the correct answer is:

**x = -5 and x = 4**.