SOLUTION: Find a polynomial f(x) of degree 4 with real coefficients and the following zeros. 1, (multiplicity 2), -2 +3i

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find a polynomial f(x) of degree 4 with real coefficients and the following zeros. 1, (multiplicity 2), -2 +3i      Log On


   

Question 1193191: Find a polynomial f(x) of degree 4 with real coefficients and the following zeros.
1, (multiplicity 2), -2 +3i
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Find a polynomial f(x) of degree 4 with real coefficients and the following zeros.
1, (multiplicity 2), -2 +3i
given: degree 4+
f%28x%29+=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29%28x-x%5B4%5D%29
zeros:
x%5B1%5D=1......... (multiplicity 2)
x%5B2%5D=-2%2B3i-> then we also have x%5B3%5D=-2-3i (complex roots always come in pairs)
f%28x%29+=%28x-1%29%28x-1%29%28x-%28-2%2B3i%29%29%28x-%28-2-3i%29%29
f%28x%29+=%28x-1%29%5E2%28x%2B2-3i%29%28x%2B2%2B3i%29
f%28x%29+=%28x%5E2+-+2x+%2B+1%29%28x%5E2%2B2x%2B3i%2Ax%2B2x%2B4%2B6i-3i%2Ax-6i-9i%5E2%29.....simplify
f%28x%29+=%28x%5E2+-+2x+%2B+1%29%28x%5E2+%2B+4+x+%2B+13%29
f%28x%29+=x%5E4+%2B+2x%5E3+%2B+6x%5E2+-+22x+%2B+13