Question

How do you write `y=5x^2+5x-3` in factored form?

Answer 1

You'll need to find the zeros first.

Explanation:

We cannot factor `y=5x^2+5x-3` by trial and error, or by AC, or by grouping.

Solve: `5x^2+5x-3 = 0` by either completing the square or by using the quadratic formula to get solutions

`x_1 = (-5+sqrt85)/10` and `x_2 = (-5-sqrt85)/10`

The factors of `5x^2+5x-3` are `x-x_1` and `x-x_2`, so we have the factored form:

`y = (x-(-5+sqrt85)/10)(x-(-5-sqrt85)/10)`

.

If you wanted vertex form, here is the answer

`y = 5(x^2+x color(white)"xxxxxx")-3`

`y = 5(x^2+x +1/4)-3-5/4`

`y = 5(x-1/2)^2 - 17/4`

Answer 2

Refer to explanation

Explanation:

First we have to find the roots of `5x^2+5x-3=0`. Hence the roots are

`x_(1,2)=(-b+-sqrt(b^2-4ac))/(2a)`

where `a=5,b=5,c=-3` so we have that

`x_(1,2)=(-b+-sqrt(b^2-4ac))/(2a)=> x_(1,2)=(-5+-sqrt(5^2+4*5*3))/10=(-5+-sqrt85)/10`

Hence the factor form is

#y=a*(x-x_1)*(x-x_2)=5*(x-(-5+sqrt85)/10)*(x-(-5-sqrt85)/10)= 1/20*(10x+5-sqrt85)*(10x+5+sqrt85)#