Question

Form a third-degree polynomial function with real coefficients such that 7 + i and -4 are zeros.

f(x)=

Answer 1

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

Answer 2

Ahhh, I see! Thank you. :-)