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

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


   

Question 891599: Find a polynomial f(x) with real coefficients having the degree and zeros.
Degree 4; zeros:3 +4i: -1 multiplicity 2
Found 2 solutions by josgarithmetic, Edwin McCravy:
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
That means the zeros are 3+4i, 3-4i, -1, and -1 again.
Those are as four zeros for the degree 2 polynomial function.

Form the polynomial starting with the factorization:
highlight%28%28x-%283%2B4i%29%29%28x-%283-4i%29%29%28x%2B1%29%5E2%29
Simplify!

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Degree 4; zeros:3 +4i: -1 multiplicity 2

x = 3+4i, x = 3-4i, x = -1, x = -1

[x-(3+4i)][x-(3-4i)][x-(-1)]² = 0

[x-3-4i][x-3+4i)][x-(-1)]² = 0

[(x-3)-4i][(x-3)+4i)][x-(-1)]² = 0

[(x-3)²-16i²][x²+2x+1) = 0

[x²-6x+9-16(-1)][x²+2x+1] = 0

[x²-6x+9+16][x²+2x+1] = 0

[x²-6x+25][x²+2x+1] = 0

x%5E4%2B2x%5E3%2Bx%5E2-6x%5E3-12x%5E2-6x%2B25x%5E2%2B50x%2B25=0

x%5E4-4x%5E3%2B14x%5E2%2B44x%2B25+=+0

Edwin