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).