SOLUTION: Solve. w^4-12w^2-2=0 I did a similar problem and was supposed to come up with 4 different radicals and I only came up with 2 for my answer and was told it was wrong.

Question 130949: Solve.
w^4-12w^2-2=0
I did a similar problem and was supposed to come up with 4 different radicals and I only came up with 2 for my answer and was told it was wrong.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let , so:

Complete the square:

or

or

But , so or

, or

, or

, or

Anytime you have a 4th degree polynomial equation, you must expect to have exactly 4 roots. They may be 4 real roots, 2 pairs of complex congujate roots, or 2 real roots and 1 pair of complex conjugate roots. Pairs of real roots might be identical (multiplicity greater than 1) but there will ALWAYS be 4 roots when the highest degree term is 4.
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