FInd the remaining zeros of f

Question

Information is given about a polynominal f(x) whose coefficants are real numbers. Find the remaining zeros of f.

Degree 4; zeros: i, -7+1

What is the remaining zero of f?

Answer 1

Polynomials with real coefficients' non-real roots come in pairs called complex conjugates: a ± bi

For example, if one of your roots were 2 + i, there would also be the root 2 - i,

because 2 + i and 2 - i are complex conjugates.

 

In your case, one of your roots is i, or maybe easier understood as 0 + i;

its complex conjugate would be 0 - i, or more simply, just -i.

 

As for -7 + 1, this is not a complex number, so there are no guarantees about a conjugate. You teacher might want the conjugate -7 - 1, but it is more likely a typo, and you meant to write -7 + i, in which case -7 - i, the complex conjugate, must be another root.