SOLUTION: Find a third degree polynomial with rational coefficients if two of its zeros are 6 and -i and it passes through the point (2,-10). Thank you in advance!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find a third degree polynomial with rational coefficients if two of its zeros are 6 and -i and it passes through the point (2,-10). Thank you in advance!      Log On


   

Question 1074483: Find a third degree polynomial with rational coefficients if two of its zeros are 6 and -i and it passes through the point (2,-10). Thank you in advance!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Rational coefficients means complex roots come in complex conjugate pairs.
f%28x%29=a%28x-6%29%28x%2Bi%29%28x-i%29
f%28x%29=a%28x-6%29%28x%5E2%2B1%29
So then find a using the point,
-10=a%282-6%29%282%5E2%2B1%29
-10=a%28-4%29%285%29
a=1%2F2
..
.
f%28x%29=%28%28x-6%29%28x%5E2%2B1%29%29%2F2
f%28x%29=x%5E3%2F2-3x%5E2%2Bx%2F2-3