SOLUTION: Find an​ nth-degree polynomial function with real​ coefficient satisfying the given conditions n=3; 1 and -2+3i are zeros; a leading coefficient of​ 1

Algebra ->  Rational-functions -> SOLUTION: Find an​ nth-degree polynomial function with real​ coefficient satisfying the given conditions n=3; 1 and -2+3i are zeros; a leading coefficient of​ 1      Log On


   

Question 1158180: Find an​ nth-degree polynomial function with real​ coefficient satisfying the given conditions
n=3; 1 and -2+3i are zeros; a leading coefficient of​ 1
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
n=3->3rd-degree polynomial function
a leading coefficient of​ 1
use zero product theorem; so polynomial function is:
f%28x%29=1%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29


given zeros:
x%5B1%5D=+1+ and
x%5B2%5D=-2%2B3i-> since complex zeros always come in pairs, you also have
x%5B3%5D=-2-3i

substitute in
f%28x%29=1%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29
f%28x%29=%28x-1%29%28x-%28-2%2B3i%29%29%28x-%28-2-3i%29%29
f%28x%29=%28x-1%29%28x%2B2-3i%29%28x%2B2%2B3i%29
f%28x%29=%28x-1%29%28x%5E2%2B2x%2B3i%2Ax%2B2x%2B4%2B6i-3ix-6i-9i%5E2%29
f%28x%29=%28x-1%29%28x%5E2%2B4x%2B4-9%28-1%29%29
f%28x%29=%28x-1%29%28x%5E2%2B4x%2B4%2B9%29
f%28x%29=%28x-1%29%28x%5E2%2B4x%2B13%29
f%28x%29=x%5E3+%2B+3x%5E2+%2B+9x+-+13