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