SOLUTION: Three roots of the polynomial equation x^4 - 4x^3 - 2x^2 + 12x + 9 = 0 are 3, -1 and -1. Explain why the fourth root must be a real number. Find the fourth root.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Three roots of the polynomial equation x^4 - 4x^3 - 2x^2 + 12x + 9 = 0 are 3, -1 and -1. Explain why the fourth root must be a real number. Find the fourth root.      Log On


   



Question 947912: Three roots of the polynomial equation x^4 - 4x^3 - 2x^2 + 12x + 9 = 0 are 3, -1 and -1. Explain why the fourth root must be a real number. Find the fourth root.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Because complex roots only occur, in polynomial with integer coefficients, as complex conjugate pairs so there would be two of them.

graph%28300%2C300%2C-5%2C5%2C-5%2C5%2Cx%5E4-4x%5E3-2x%5E2%2B12x%2B9%29
x=-3