Find the zeros of:

`y=4x^3+4x^2-7x+2`

``

I need to know how to do the work. PLEASE HELP!

Expert Answers

An illustration of the letter 'A' in a speech bubbles

`4x^3 +4x^2 - 7x +2 = 0`

1) We will rewrite -7x = -x -6x then we will re-arrange terms.

`4x^3 + 4x^2 -x -6x +2 = 0`

`(4x^3 -x) + (4x^2 -6x+2)= 0`

`x(4x^2-1) + (2x-1)(2x-2) = 0`

`x(2x-1)(2x+1) + (2x-1)(2x-2)= 0`

`(2x-1) ( x(2x+1) + (2x-2)= 0`

`==> (2x-1)(2x^2 + x + 2x -2)= 0`

`==> (2x-1)(2x^2 +3x -2)= 0`

`==> (2x-1)(2x-1)(x+2)= 0`

`==> (2x-1)^2 (x+2)= 0`

`==> x = 1/2 `

`==> x = -2`

`==> x = (1/2, -2}`

2) We try to substitute the factor of 2 = -1, 1, -2, and 2 to find possible zeros.

`==> x = -2 ==> y(-2)= 0`

Then x = -2 is a zero of y, then, (x+2) is a factor.

`==> (4x^3+4x^2 -7x+2) = (x+2)(4x^2 -4x+1)`

`==> (4x^3 +4x^2 -7x+2)= (x+2)(2x-1)^2`

`==> x1= -2`

`==> x2= 1/2`

`==> x = {-2, 1/2}`

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial