SOLUTION: Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 4; zeros: 3, multiplicity 2; 4i f(x)=a(___________ ______)

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


   

Question 957105: Form a polynomial f(x) with real coefficients having the given degree and zeros.
Degree 4; zeros: 3, multiplicity 2; 4i
f(x)=a(__________________)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given:
Degree 4;
zeros:
3, multiplicity 2;
4i, then you also have -4i (complex roots always come in pairs)
use zero product formula:
f%28x%29=a%28%28x-3%29%5E2%28x-4i%29%28x%2B4i%29%29
f%28x%29=a%28%28x%5E2-6x%2B9%29%28x%5E2%2B4i%2Ax-4i%2Ax-16i%5E2%29%29
f%28x%29=a%28%28x%5E2-6x%2B9%29%28x%5E2-16%28-1%29%29%29
f%28x%29=a%28%28x%5E2-6x%2B9%29%28x%5E2%2B16%29%29
f%28x%29=a%28x%5E4-6x%5E3%2B25x%5E2-96x%2B144%29