SOLUTION: And this is similar (I think) to my last post...Help Please!! Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 4; zeros: 2, multiplicity

Algebra ->  Rational-functions -> SOLUTION: And this is similar (I think) to my last post...Help Please!! Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 4; zeros: 2, multiplicity       Log On


   

Question 970036: And this is similar (I think) to my last post...Help Please!!
Form a polynomial f(x) with real coefficients having the given degree and zeros.
Degree 4; zeros: 2, multiplicity 2; 3i

I truly do not understand any of this...Thank you for any help!!
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Form a polynomial f%28x%29 with real coefficients having the given degree and zeros.
Degree 4;
zeros:
x%5B1%5D=2, multiplicity 2; =>use it two times, or square it
x%5B2%5D=3i=>we also have x%5B3%5D=-3i because complex zeros come always in pairs
then, using zero product rule, f%28x%29 will be:
f%28x%29=%28x-x%5B1%5D%29%5E2%28x-x%5B2%5D%29%28x-x%5B3%5D%29
f%28x%29=%28x-2%29%5E2%28x-3i%29%28x-%28-3i%29%29
f%28x%29=%28x%5E2-4x%2B4%29%28x-3i%29%28x%2B3i%29
f%28x%29=%28x%5E2-4x%2B4%29%28x%5E2-%283i%29%5E2%29
f%28x%29=%28x%5E2-4x%2B4%29%28x%5E2-9i%5E2%29
f%28x%29=%28x%5E2-4x%2B4%29%28x%5E2-9%28-1%29%29
f%28x%29=%28x%5E2-4x%2B4%29%28x%5E2%2B9%29
f%28x%29=x%5E4-4x%5E3%2B4x%5E2%2B9x%5E2-36x%2B36
f%28x%29=x%5E4-4x%5E3%2B13x%5E2-36x%2B36

+graph%28+600%2C+600%2C+-10%2C10%2C+-10%2C+50%2C+x%5E4-4x%5E3%2B13x%5E2-36x%2B36%29+