SOLUTION: A degree 4 polynomial with integer coefficients has zeros −1, −3i and 1, with 1 a zero of multiplicity 2. If the coefficient of x^4 is 1, then the polynomial is Th

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A degree 4 polynomial with integer coefficients has zeros −1, −3i and 1, with 1 a zero of multiplicity 2. If the coefficient of x^4 is 1, then the polynomial is Th      Log On


   

Question 1001720: A degree 4 polynomial with integer coefficients has zeros −1, −3i and 1, with 1 a zero of multiplicity 2. If the coefficient of x^4 is 1,
then the polynomial is
This is what I did so far
(x+1)(x-3i)(x-1)^2, but it is being marked as incorrect.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

4 polynomial with integer coefficients has zeros:
-1,and 1, with 1 a zero of multiplicity 2,=>%28x%2B1%29%5E2
if you know that polynomial is degree 4 polynomial, you cannot have %28x-1%29%5E2; that will make your polynomial a polynomial of degree 5 because
if -3i is a zero, don't forget that complex zeros always come in pairs; so, you have 3i too


f%28x%29=%28x%2B1%29%5E2%28x-3i%29%28x%2B3i%29
f%28x%29=%28x%2B1%29%5E2%28x%5E2-%283i%29%5E2%29
f%28x%29=%28x%5E2%2B2x%2B1%29%28x%5E2-9%28i%29%5E2%29
f%28x%29=%28x%5E2%2B2x%2B1%29%28x%5E2-9%28-1%29%29
f%28x%29=%28x%5E2%2B2x%2B1%29%28x%5E2%2B9%29
f%28x%29=x%5E4%2B2x%5E3%2B1x%5E2%2B9x%5E2%2B18x%2B9
f%28x%29=x%5E4%2B2x%5E3%2B10x%5E2%2B18x%2B9

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E4%2B2x%5E3%2B10x%5E2%2B18x%2B9%29+