What are the zeros of the function y = 2x2 – 3x – 20, and why? a. the zeros are x = – 5 2 and x = 4 because in factored form, the function is y = (2x – 5)(x + 4). b. the zeros are x = – 5 2 and x = 4 because in factored form, the function is y = (2x + 5)(x – 4). c. the zeros are x = 5 2 and x = –4 because in factored form, the function is y = (2x – 5)(x + 4). d. the zeros are x = 5 2 and x = –4 because in factored form, the function is y = (2x + 5)(x – 4)?

The correct answer is B) the zeros are x= -5/2 and x=4 because in factored form the equation is y=(2x+5)(x-4).

To factor this, we want factors of a*c that sum to b:
a*c = 2(-20) = -40
b = -3

Factors of -40 that sum to -3 would be -8 and 5.  This tells us how to "split up" bx:
y=2x²-8x+5x-40

Now we group together the first two terms and the last two terms:
y=(2x²-8x)+(5x-40)

We factor out the GCF of each term:
y=2x(      )+5(      )

When we factor 2x out of 2x², we have x left; factoring 2x out of -8x gives us -4:
y=2x(x-4)+5(      )

Factoring 5 out of 5x leaves us x; factoring 5 out of -20 leaves us -4:
y=2x(x-4)+5(x-4)

The GCF of each piece now is x-4; factoring this out, we have
y=(x-4)(2x+5)

Using the zero product property, we know that either x-4=0 or 2x+5=0:
x-4=0
x-4+4=0+4
x=4

2x+5=0
2x+5-5=0-5
2x=-5
2x/2 = -5/2
x=-5/2