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

f(x)=

Question

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

campbell_st · Answer

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

anonymous · Answer

Ahhh, I see! Thank you. :-)