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1. Prove that 1+i is a root of equation z^4+3z^2-6z+10=0. Find all the other roots.
2. (Original post by Vneezus)
Prove that 1+i is a root of equation z^4+3z^2-6z+10=0. Find all the other roots.
How do you prove that 1+i is a root?

What does this immediately tell you another root is?
3. By substituting (1+i) instead of z and checking if it equals zero.
4. (Original post by Vneezus)
By substituting (1+i) instead of z and checking if it equals zero.
Indeed that is a way of checking whether it is a root. Then you should be able to find another root related to this one because the coefficients of the polynomial are real. Once you have the other root you can deduce the quartic into a product of 2 linear and 1 quadratic polynomials and solve the quadratic as usual to get your 2 last roots.
5. (Original post by RDKGames)
Indeed that is a way of checking whether it is a root. Then you should be able to find another root related to this one because the coefficients of the polynomial are real. Once you have the other root you can deduce the quartic into a product of 2 linear and 1 quadratic polynomials and solve the quadratic as usual to get your 2 last roots.
Thanks man that really helped!

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Updated: January 12, 2017
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