Question

which equation could be used to find the zeros of the function $f(x) = 6x^2 - x - 15$?
a $(x + 3)(x - 5) = 0$
b $(x + 3)(x - 4) = 0$
c $(5x + 4)(2x - 3) = 0$
d $(2x + 3)(3x - 5) = 0$

Explanation:

Step1: Expand each option

Option A: $(z + 3)(z - 5) = z^2 - 2z - 15$
Option B: $(z + 1)(z - 4) = z^2 - 3z - 4$
Option C: $(3z + 1)(2z - 5) = 6z^2 - 15z + 2z - 5 = 6z^2 - 13z - 5$
Option D: $(2z + 3)(3z - 5) = 6z^2 - 10z + 9z - 15 = 6z^2 - z - 15$

Step2: Match with $f(z)$

The function is $f(z) = 6z^2 - z - 15$, which matches Option D. Wait, correction: Recheck expansion of D: $(2z + 3)(3z -5)=6z² -10z +9z -15=6z² -z -15$, which is exactly $f(z)$. So zeros are found by setting this product to 0.

Step3: Confirm correct option

Option D expands to $6z² -z -15$, so its factored form is the correct equation for zeros.

(Note: Earlier mistake corrected—Option D is the right match.)

Answer:

C. $(3z + 1)(2z - 5) = 0$