Question

Simone found that −5 is the root of the equation 3x2 + 14x − 5 = 0. Which statements are true? Select all that apply.

A. −5 is an x-intercept of the graph of the function y = 3x2 + 14x − 5.
B.−5 is a zero of the function y = 3x2 + 14x − 5.
C.(x − 5) is a factor of 3x2 + 14x − 5.
D. (x + 5) is a factor of 3x2 + 14x − 5.

Answer 1

A, B, D

Explanation:

You want to know the correct statements about the root -5 of the equation 3x² +14x -5 = 0.

A. x-intercept

A "root" and an "x-intercept" generally refer to the same thing. These are values that make the expression zero. (The x-axis is y=0, so an intersection with the x-axis will be where the function value is zero.)

If -5 is a root, -5 is an x-intercept of the graph of y=3x² +14x -5.

B. zero

See A above. -5 is a zero of the function y=3x² +14x -5.

C. (x -5)

A zero or x-intercept corresponds to a factor whose value is zero at that point. The factor x-5 is not zero at x=-5, so it is not a factor of the function.

D. (x +5)

The factor (x +5) is zero at x = -5, so (x +5) is a factor of 3x² +14x -5.