anonymous one year ago Form a third-degree polynomial function with real coefficients such that 7 + i and -4 are zeros. f(x)=

1. campbell_st

well one of the factors is a quadratic with complex roots so start with that the roots is $x = 7 \pm i$ subtract 7 from both sides of the equation. $x - 7 = \pm i$ square both sides of the equation $(x -7)^2 = i^2$ you need to remember i^2 = -1 so then its $(x -7)^2 = -1~~~or~~~~(x -7)^2 + 1 = 0$ so you need to simplify $(x -7)^2 + 1$ to get the quadratic factor. the linear factor is when x = -4 or x + 4 is the linear factor... then the polynomial is $P(x) = (x +4)[(x - 7)^2 + 1]$ simplify the equation

2. anonymous

Ahhh, I see! Thank you. :-)