Which factorizations can be used to identify the real zeros of the function f(x)=-20x^2 - 23x-6? Select the correct answer from the following Show your work.
a) (-10x+2)(2x+3)
b) -(10x +2)(2x-3)
c) -(4x-3)(5x+2)
d) -(4x-3)(5x-2)
To find the real zeros of the function f(x) = -20x^2 - 23x - 6, we need to set f(x) equal to zero:
-20x^2 - 23x - 6 = 0
Now, we need to factor the quadratic expression. Looking at the factors provided, we see that option d) -(4x-3)(5x-2) can be used to find the roots.
-(4x-3)(5x-2) = 0
Setting each factor to zero, we get:
4x - 3 = 0 or 5x - 2 = 0
Solving these equations gives the roots:
4x = 3 or 5x = 2
x = 3/4 or x = 2/5
Therefore, the real zeros of the function f(x) = -20x^2 - 23x - 6 are x = 3/4 and x = 2/5. So, the correct answer is d) -(4x-3)(5x-2).