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?

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- Oct 26th 2009, 09:28 AMtsmithFind 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? - Oct 26th 2009, 10:15 AMmasters
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 $\displaystyle x^2+1$

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

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

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