SOLUTION: find a polynomial function of degree 3 with zeros of x=2 and x=2+3i.expand the polynomial by multiplying the factors,write the answer in the form f(x)=ax^3+bx^2+cx+d , lead coeff

Question 676170: find a polynomial function of degree 3 with zeros of x=2 and x=2+3i.expand the polynomial by multiplying the factors,write the answer in the form f(x)=ax^3+bx^2+cx+d , lead coefficient can be +or- 1. all i know is that one factor is (x-2) and one factor is (2-3i) but i dont know what that gets me????????
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

If a polynomial with real coefficients has a complex zero, then the conjugate of that complex zero is also a zero. Hence, if 2 + 3i is a zero, 2 - 3i is also a zero.

Then your factors are:

Multiply the three factors and then collect terms to derive your 3rd degree polynomial. Hint for ease of computation: Consider the complex numbers to be a single number and remember that the product of two conjugates is the difference of two squares but that since

the product of two complex conjugates becomes the sum of two squares. Write back and I'll let you know if your answer is correct.

John

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