# Thread: Find all of the real and imaginary zeros for the polynomial function

1. ## [Solved]Find all of the real and imaginary zeros for the polynomial function

Find all of the real and imaginary zeros for the polynomial function f(x)=x^3-7x^2+x-7 Answer is 7,-i,i How do I solve this to get to the answer

2. Originally Posted by ToXic01
Find all of the real and imaginary zeros for the polynomial function f(x)=x^3-7x^2+x-7 Answer is 7,-i,i How do I solve this to get to the answer
Factor by grouping

$\displaystyle x^3 - 7x^2 + x - 7 = x^2(x - 7) + (x - 7)$

$\displaystyle = (x - 7)(x^2 + 1)$

Now do you see how to get to the answer?

3. $\displaystyle x^3-7x^2+x-7=x^2(x-7)+(x-7)=(x-7)(x^2+1)$

4. Originally Posted by Jhevon
Factor by grouping

$\displaystyle x^3 - 7x^2 + x - 7 = x^2(x - 7) + (x - 7)$

$\displaystyle = (x - 7)(x^2 + 1)$

Now do you see how to get to the answer?
so if i set this equal to zero i get the answer

5. Originally Posted by ToXic01
so if i set this equal to zero i get the answer
Yep make $\displaystyle x^2 + 1=0$ and $\displaystyle x - 7=0$