Posted by **Veronica** on Tuesday, November 10, 2009 at 5:31pm.

what is the root of 4x to the 4th power + 8x to the 3rd power - 13x to the 2nd power -2x +3

- math/ college algebra -
**Reiny**, Tuesday, November 10, 2009 at 5:40pm
I think you mean

(√(4x))^4 + 8x^3 - 13x^2 - 2x + 3

which is

16x^2 + 8x^3 - 13x^2 - 2x + 3

= 8x^3 + 3x^2 - 2x + 3

Now what about it?

What do want done with it?

- math/ college algebra -
**Veronica**, Tuesday, November 10, 2009 at 5:44pm
I need the roots of 4x^4+8x^3-13x^2-2x+3

- math/ college algebra -
**Reiny**, Tuesday, November 10, 2009 at 5:54pm
Read your first line, can you see how it can be misinterpreted?

so let

f(x) = 4x^4+8x^3-13x^2-2x+3

try x = ±1, ±3

f(1) = 0, so x-1 is a factor,

I then used synthetic division to show that

4x^4+8x^3-13x^2-2x+3 = (x-1)(4x^3 + 12x^2 - x - 3)

but (4x^3 + 12x^2 - x - 3)

= 4x^2(x+3) - (x+3)

= (x+3)(4x^1 - 1)

= (x+3)*2x-1)(2x+1)

so for

4x^4+8x^3-13x^2-2x+3 = 0

(x-1)x+3)(2x+1)(2x-1) = 0

x = 1, -3, ±1/2

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