Question

One of the solutions to the equation x3+5x2+10x+50=0
is −5
. Find the full solution set. Which is the following options correctly describes the solution set?(1 point)
Responses

It has one real solution and two non-real solutions.
It has one real solution and two non-real solutions.

It has one non-real solution and two real solutions.
It has one non-real solution and two real solutions.

It has three real solutions.

Answer 1

Divide by (x + 5). Synthetic division gives quotient x^2 + 10, so

x^3 + 5x^2 + 10x + 50 = (x + 5)(x^2 + 10).

Solve x^2 + 10 = 0 → x = ± i√10.

Full solution set: {−5, i√10, −i√10}.

Thus: It has one real solution and two non-real solutions.