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

Algebra.Com
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)   (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:

Simplify!
Answer by Edwin McCravy(20060)   (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





Edwin
RELATED QUESTIONS

Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree... (answered by MathLover1)
Form a polynomial​ f(x) with real coefficients having the given degree and zeros.... (answered by josgarithmetic)
Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree; (answered by Fombitz)
Form a polynomial f(x) with real coefficients having the given degree and zeros.... (answered by Alan3354)
Form a polynomial f(x) with real coefficients having the given degree and zeros Degree 4; (answered by Boreal)
Find a polynomial f(x) of degree 4 with real coefficients and the following zeros... (answered by ikleyn)
Form a polynomial f(x) with real coefficients having the given degree and zeros Degree (answered by ikleyn)
Form a polynomial f(x) with real coefficients having the given degree and zeros... (answered by Alan3354)
Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree (answered by swincher4391)