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