Use the discriminant to find what type of solutions (two rational, two irrational, one rational, or two nonreal complex)
each of the following equations has. Do not solve the equation.
-$x ^ { 2 } - 2 x + 8 = 0$
A) two rational solutions
B) two irrational solutions
C) two nonreal complex solutions
D) one rational solution

Question

Quizplus · Accepted Answer

The discriminant of a quadratic equation $ax^2 + bx + c = 0$ is given by $b^2 - 4ac$. For the equation $x^2 - 2x + 8 = 0$, the discriminant is $(-2)^2 - 4(1)(8) = 4 - 32 = -28$. Since the discriminant is negative, the equation has two nonreal complex solutions.

Use the Discriminant to Find What Type of Solutions (Two x2−2x+8=0x ^ { 2 } - 2 x + 8 = 0x2−2x+8=0

Use the Discriminant to Find What Type of Solutions (Two $x ^ { 2 } - 2 x + 8 = 0$