SOLUTION: find the polynomial with leading coefficient -2, that has degrees 3 and roots 2 and 3i

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: find the polynomial with leading coefficient -2, that has degrees 3 and roots 2 and 3i      Log On


   

Question 1000823: find the polynomial with leading coefficient -2, that has degrees 3 and roots 2 and 3i
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
find the polynomial with
,
that has degrees 3

f%28x%29=ax%5E3%2Bbx%5E2%2Bcx%2Bd
leading coefficient a=-2
roots
x%5B1%5D=2 and x%5B2%5D=3i => x%5B2%5D=-3i
then we have:
f%28x%29=%28-2x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29
f%28x%29=-2%28x-2%29%28x-3i%29%28x%2B3i%29
f%28x%29=-2%28x-2%29%28x%5E2-%283i%29%5E2%29
f%28x%29=-2%28x-2%29%28x%5E2-9%28i%29%5E2%29
f%28x%29=-2%28x-2%29%28x%5E2-9%28-1%29%29
f%28x%29=-2%28x-2%29%28x%5E2%2B9%29
f%28x%29=-2%28x%5E3%2B9x-2x%5E2-18%29
f%28x%29=-2x%5E3%2B4x%5E2-18x%2B36

+graph%28+600%2C+600%2C+-10%2C+10%2C+-200%2C+200%2C+-2x%5E3%2B4x%5E2-18x%2B36%29+