Which factorizations can be used to identify the real zeros of the function f(x) = -20x^2 + 23x - 6?
show your work
A (-10x + 2) (2x + 3)
B -(10x + 2)(2x — 3)
C -(4x - 3)(5x + 2)
D -(4x - 3)(5x - 2)
To identify the real zeros of the function f(x) = -20x^2 + 23x - 6, we need to find the values of x that make the function equal to zero.
First, let's factor the quadratic function:
f(x) = -20x^2 + 23x - 6
= -(20x^2 - 23x + 6)
We can factor -20x^2 - 23x + 6 by finding two numbers that multiply to -20 * 6 = -120 and add up to -23. The two numbers are -15 and -8.
= -(20x^2 - 15x - 8x + 6)
= -(5x(4x - 3) - 2(4x - 3))
= -(5x - 2)(4x - 3)
Now we need to set the function equal to zero:
-(5x - 2)(4x - 3) = 0
To find the zeros, we set each factor equal to zero and solve for x:
5x - 2 = 0
5x = 2
x = 2/5
4x - 3 = 0
4x = 3
x = 3/4
Therefore, the real zeros of the function f(x) = -20x^2 + 23x - 6 are x = 2/5 and x = 3/4. The factorization -(5x - 2)(4x - 3) can be used to identify these zeros.
Therefore, the correct answer is A (-10x + 2) (2x + 3).