# Find the solution set?

• October 26th 2009, 09:28 AM
tsmith
Find the solution set?
Use the given root to find the solution set of the polynomial.
Polynomial: x^4 - 4x^3 + 2x^2 - 4x + 1 = 0
Given root: i

How do I solve this problem?
• October 26th 2009, 10:15 AM
masters
Quote:

Originally Posted by tsmith
Use the given root to find the solution set of the polynomial.
Polynomial: x^4 - 4x^3 + 2x^2 - 4x + 1 = 0
Given root: i

How do I solve this problem?

Hi tsmith,

If one of the roots is i, then one of the roots is also -i.

(x - i) and (x + i) are factors.

Their product is $x^2+1$

Use polynomial long division on your original function to find the depressed quadratic.

I think you'll discover it's $x^2-4x+1$

Now, use the quadratic formula to discover the last two roots.