SOLUTION: Form a polynomial f(x) with real coefficients having the given degree and zeros: Degree; zeros: -4-2i; 1 multiplicity 2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Form a polynomial f(x) with real coefficients having the given degree and zeros: Degree; zeros: -4-2i; 1 multiplicity 2      Log On


   

Question 957068: Form a polynomial f(x) with real coefficients having the given degree and zeros:
Degree; zeros: -4-2i; 1 multiplicity 2
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29 with real coefficients having the given degree and zeros:
Degree;
zeros:
x%5B1%5D=-4-2i;complex roots coming always in pairs, so you also have x%5B2%5D=-4%2B2i
x%5B3%5D=1 multiplicity 2-double root
use zero product rule to find f%28x%29
f%28x%29=%28x-%28-4-2i%29%29%28x-%28-4%2B2i%29%29%28x-1%29 since %28x-1%29 has multiplicity 2 we can square it
f%28x%29=%28x%2B4%2B2i%29%28x%2B4-2i%29%28x-1%29%5E2

f%28x%29=%28x%5E2%2B8x%2B16-4%28-1%29%29%28x%5E2-2x%2B1%29
f%28x%29=%28x%5E2%2B8x%2B16%2B4%29%28x%5E2-2x%2B1%29
f%28x%29=%28x%5E2%2B8x%2B20%29%28x%5E2-2x%2B1%29
f%28x%29=x%5E4%2B8x%5E3%2B20x%5E2-2x%5E3-16x%5E2-40x%2Bx%5E2%2B8x%2B20
f%28x%29=x%5E4%2B6x%5E3%2B5x%5E2-32x%2B20