One root of the polynomial equation 0 = x3 – 5x2 – 24x + 130 is 5 + i. Find an additional root.

37. One root of the polynomial equation 0 = x3 – 5x2 – 24x + 130 is 5 + i. Find an additional root.

A. –5 + i
B. –1 + 5i
C. 1 + 5i
D. 5 – i

d. 5 - i

As the other Answerer stated already. The reason though, that's the useful thing. When you have a complex root to ANY equation, the root's conjugate is ALWAYS a root too. So if you have "5 + i" its conjugate, "5 - i", must be a root too.

That's why the question gave you the root it did. It was trying to see if you remembered that fact. Oh, -5 is the third root if interested. But if you give that as your answer, your teacher will bug you about 5 - i.

You can answer all of these questions easily by looking.

If a+bi is the root of any polynomial with real coefficients, then a-bi is a second root of the same polynomial.

Answer D. 5 - i