SOLUTION: Write a third degree polynomial function y=P(x) with rational coefficients so that P(x)=0 has the given roots. 1, 2-i 3, 6+i 3i, 7 1, 5i 3, -4i

Question 819497: Write a third degree polynomial function y=P(x) with rational coefficients so that P(x)=0 has the given roots.
1, 2-i
3, 6+i
3i, 7
1, 5i
3, -4i
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Write a third degree polynomial function y=P(x) with rational coefficients so that P(x)=0 has the given roots.
1, 2-i and 2+i
-----
P(x) = (x-1)(x-2+i)(x-2-i)
----
= (x-1)[(x-2)+i)(x-2)-i)]
----
= (x-1)[(x-2)^2+1]
----
= (x-1)(x^2-4x+5)
----
= x^3 - 5x^2 + 9x -5
======================
Cheers,
Stan H.
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3, 6+i
3i, 7
1, 5i
3, -4i

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