math/ college algebra
posted by Veronica .
what is the root of 4x to the 4th power + 8x to the 3rd power  13x to the 2nd power 2x +3

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? 
I need the roots of 4x^4+8x^313x^22x+3

Read your first line, can you see how it can be misinterpreted?
so let
f(x) = 4x^4+8x^313x^22x+3
try x = ±1, ±3
f(1) = 0, so x1 is a factor,
I then used synthetic division to show that
4x^4+8x^313x^22x+3 = (x1)(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)*2x1)(2x+1)
so for
4x^4+8x^313x^22x+3 = 0
(x1)x+3)(2x+1)(2x1) = 0
x = 1, 3, ±1/2