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

#### ToXic01

[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

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#### Jhevon

MHF Helper
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?

#### Plato

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

#### ToXic01

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

#### pickslides

MHF Helper
so if i set this equal to zero i get the answer
Yep make $$\displaystyle x^2 + 1=0$$ and $$\displaystyle x - 7=0$$