SOLUTION: what is the equation that has zeros at 4 and 2+5i

Question 697552: what is the equation that has zeros at 4 and 2+5i
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
what is the equation that has zeros at 4 and 2+5i
.
Based on the zeros, factors must be:
(x-4)(x+2+5i)(x+2-5i)
just multiply the above together to get your equation:
(x-4)(x(x+2-5i)+2(x+2-5i)+5i(x+2-5i))
(x-4)(x^2+2x-5xi+2x+4-10i+5xi+10i-25)
(x-4)(x^2+4x-5xi+4-10i+5xi+10i-25)
(x-4)(x^2+4x+4-10i+10i-25)
(x-4)(x^2+4x+4-25)
(x-4)(x^2+4x-21)
x^2(x-4)+4x(x-4)-21(x-4)
x^3-4x^2+4x^2-16x-21x+84
x^3-16x-21x+84
x^3-37x+84

RELATED QUESTIONS
Find the equation for a parabola that has zeros at - 6 and 4 and passes through the point (answered by ankor@dixie-net.com)

What is the degree of the simplest polynomial with integger coefficients that has square... (answered by josmiceli)

Suppose that a polynomial function of degree 5 with rational coefficients has 0 (with... (answered by solver91311)

S has degree 4 and zeros 4i and... (answered by fractalier)

n=3; 4 and 5i are zeros;... (answered by ikleyn)

Form a polynomial f(x) with real coefficients having the given degree and zeros.... (answered by Alan3354)

Find a polynomial with integer coefficients that has degree 4, zeros 5i and 1+i, and... (answered by josgarithmetic)

Hello! I am suppose to write a polynomial function with the following. Degree 4,... (answered by Fombitz)

I am having the most difficult time figuring out how to format this into a polynomial. I... (answered by josgarithmetic,Theo)