# SOLUTION: Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 4; zeroes: -3-2i; -2 multiplicity 2 So what i've done so far (x+(3-2i))(x+(3+2i))(x

Algebra ->  -> SOLUTION: Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 4; zeroes: -3-2i; -2 multiplicity 2 So what i've done so far (x+(3-2i))(x+(3+2i))(x      Log On

 Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Mathway solves algebra homework problems with step-by-step help!

 Click here to see ALL problems on Polynomials-and-rational-expressions Question 596416: Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 4; zeroes: -3-2i; -2 multiplicity 2 So what i've done so far (x+(3-2i))(x+(3+2i))(x+2)^2 Now my algebra teacher taught me a shortcut on the i's. (x+3)(-2i)(x+3)(2i)(x+2)^2 (x+3)^2 = x^2 + 6x + 9 / (-2i)(2i) = -4i^2 = 4 / (x+2)^2 = x^2 + 4x + 4 after all of that I have a huge problem just multiplying the quadratics together so I will give you what I had as an answer and if you can guide me in the wrong direction on my sign mistakes. (x^2+6x+9)(x^2+4x+4)+4 (x^4+4x^3+4x^2+6x^3+24x^2+24x+9x^2+36x+36) x^4+10x^3+37x^2+60x+36 I have a feeling it's my final multiplication or the negative and positive im getting wrong. By the way im suppose to get a polynomial answer.Answer by stanbon(60778)   (Show Source): You can put this solution on YOUR website!Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 4 zeroes: -3-2i; -2 multiplicity 2 f(x) = (x-(-3-2i))(x-(-3+2i))(x+2)^2 ------- Rearrange: f(x) = ((x+3)+2i)((x+3)-2i)(x+2)^2 ------- f(x) = [(x+3)^2+4)(x^2+4x+4) ----- f(x) = (x^2+6x+13)(x^2+4x+4) --------------------------------------- Cheers, Stan H.