Pre-Calc: A polynomial with a specified complex zero

Question

Hello! I am currently stuck on a homework question and I keep getting it wrong. Here is what the question is asking:

Find a polynomial with integer coefficients that satisfies the given conditions.

R has degree 4 and zeros 3 − 3i and 2, with 2 a zero of multiplicity 2.

Here is the work that I have done:

(x-2)(x-2)(x+3+3i)(x+3-3i)

(x-2)(x-2)[(x+3)+3i][(x+3)-3i]

(x-2)(x-2)[(x+3)²-(3i)²]

(x-2)(x-2)[(x+3)²-(-9)]

(x²-4x+6)(x²+6x+18)

x⁴+2x³-2x²-48x+72

So R(x)=x⁴+2x³-2x²-48x+72

When I go to check it it says it's wrong. I have checked the math over and over and have done it 4 time but end up with the same answer. I appreciate your time in advance!

Answer 1

You have zeroes of 2 (multiplicity 2) and 3 ± 3i. Thses zeros give you factors of:

(x-2)*(x-2)*(x-3-3i)*(x-3+3i) (note x MINUS 3 ...)

See if this gives you the correct answer.

Hope this helps!

Answer 2

You did make a minor error. What is (x-2) (x-2)? It is x² - 4x + 4, not x² - 4x + 6 Plug the corrected value in and I get:

x⁴ - 2x³ - 2x² - 48x + 72 Hope this helps. Sometimes you get so close to a problem, you repeat the same error over and over. You had the basics down cold!!!