Question

A polynomial function g(x) has real roots at x =-3 and x = 2/3. Which is a 1 point

possible equation for the function?
A. I don't know
B. g(x) = 3(x - 3)(x + 2)
C. g(x) = -2(x + 3) (3x − 2)
D. g(x) = (x − 3)(x + 2)
E. g(x) = (x+3)(2x - 3)

Answer 1

The correct polynomial function with real roots at x = -3 and x = 2/3 is g(x) = -2(x + 3)(3x - 2), so the answer is C.

Step-by-step explanation:

The student's question is asking for the correct polynomial function that has real roots at x = -3 and x = 2/3. We can directly eliminate any options that do not have factors corresponding to these roots.

A polynomial with these roots will have factors of (x + 3) and (x - 2/3), or equivalently (3x - 2) when we clear the fraction.

The correct equation that corresponds to these roots is given by:

g(x) = -2(x + 3) (3x - 2)

Therefore, the correct answer is C. g(x) = -2(x + 3)(3x - 2).