Question

Given g(x) = x ^ 2 - 3x - 10 , which statement is true? The zeros are 5 and -2, because the factors are (x - 5) and (x + 2) The zeros are -5 and -2, because the factors are (x + 5) and (x + 2) The zeros are 2 and -5, because the factors are (x - 2) and (x + 5) The zeros are 2 and 5, because the factors are (x - 2) and (x - 5)

Answer 1

To find the zeros of the function \( g(x) = x^2 - 3x - 10 \), we can factor the quadratic expression or use the quadratic formula.

1. We look for two numbers that multiply to \(-10\) (the constant term) and add to \(-3\) (the coefficient of the \(x\) term). The numbers \(-5\) and \(2\) meet this requirement:
\[
-5 \times 2 = -10 \quad \text{and} \quad -5 + 2 = -3.
\]

2. So we can factor the quadratic function as:
\[
g(x) = (x - 5)(x + 2).
\]

3. The zeros of the function can be found by setting \(g(x) = 0\):
\[
(x - 5)(x + 2) = 0.
\]

4. This gives us the solutions:
\[
x - 5 = 0 \quad \Rightarrow \quad x = 5,
\]
\[
x + 2 = 0 \quad \Rightarrow \quad x = -2.
\]

Thus, the zeros of the function \( g(x) \) are \( 5 \) and \( -2 \).

Therefore, the true statement is:
**The zeros are 5 and -2, because the factors are (x - 5) and (x + 2).**