MATH SOLVE

2 months ago

Q:
# 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)?

Accepted Solution

A:

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

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