SOLUTION: Form a polynomial f(x)with real coefficients having the given degree and zeros. degree 4; zeros: 2-5i ;3 multiplicity 2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Form a polynomial f(x)with real coefficients having the given degree and zeros. degree 4; zeros: 2-5i ;3 multiplicity 2      Log On


   

Question 1152855: Form a polynomial f(x)with real coefficients having the given degree and zeros.
degree 4; zeros: 2-5i ;3 multiplicity 2
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-%282-5i%29%29%28x-%282%2B5i%29%29%28x-3%29%28x-3%29
Simplify. Do what you have to.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
given:
degree 4;
zeros:
x%5B1%5D=2-5i => complex zeros always come in pairs, and you also have
x%5B2%5D=2%2B5i
x%5B3%5D=3-> multiplicity 2; comes two times
x%5B4%5D=3
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29%28x-x%5B4%5D%29
f%28x%29=%28x-%282-5i%29%29%28x-%282%2B5i%29%29%28x-3%29%28x-3%29
f%28x%29=%28x-2%2B5i%29%28x-2-5i%29%28x-3%29%5E2
f%28x%29=%28x%5E2+-+4+x+%2B+29%29%28x%5E2-6x%2B9%29
f%28x%29=x%5E4+-+10+x%5E3+%2B+62+x%5E2+-+210+x+%2B+261