Question

Given g(x)=x²-3x - 10, which statement is true?

A. The zeros are 5 and -2, because the factors are
(x - 5) and (x + 2)

B. The zeros are -5 and -2, because the factors are
(x + 5) and (x + 2).

C. The zeros are 2 and -5, because the factors are
(x - 2) and (x + 5).

D. 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), we need to set g(x) equal to zero and solve for x.

g(x) = x² - 3x - 10 = 0

To solve for x, we can use the quadratic formula:

x = (-b ± sqrt(b² - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.

In this case, a = 1, b = -3, and c = -10.

x = (-(-3) ± sqrt((-3)² - 4(1)(-10))) / 2(1)

x = (3 ± sqrt(49)) / 2

x = (3 ± 7) / 2

So the two zeros of the function g(x) are x = 5 and x = -2.

Therefore, the correct answer is A: The zeros are 5 and -2, because the factors are (x - 5) and (x + 2).