Use the discriminant to determine whether the equation has two non real complex solutions, one real solution with a multiplicity of two, or two real solutions. Match each of the equations with the number of decisions to obtain a true statement.
-$\text { two nonreal complex solutions }$
A) $x ^ { 2 } + 10 x - 24 = 0$
B) $4 x ^ { 2 } + 12 x + 9 = 0$
C) $4 x ^ { 2 } - x + 9 = 0$

Question

Use the discriminant to determine whether the equation has two non real complex solutions, one real solution with a multiplicity of two, or two real solutions. Match each of the equations with the number of decisions to obtain a true statement.
-$\text { two nonreal complex solutions }$ 
A) $x ^ { 2 } + 10 x - 24 = 0$ 
B) $4 x ^ { 2 } + 12 x + 9 = 0$ 
C) $4 x ^ { 2 } - x + 9 = 0$

Quizplus · Accepted Answer

BThe discriminant of a quadratic equation $ax^2 + bx + c = 0$ is given by $b^2 - 4ac$. If the discriminant is positive, the equation has two real solutions. If it is zero, there is one real solution with a multiplicity of two. If it is negative, the equation has two nonreal complex solutions. For option C, the discriminant is $(-1)^2 - 4(4)(9) = 1 - 144 = -143$, which is negative, indicating two nonreal complex solutions. For option B, the discriminant is $12^2 - 4(4)(9) = 144 - 144 = 0$, indicating one real solution with a multiplicity of two. Option A is not mentioned because its discriminant is positive, indicating two real solutions.

Use the Discriminant to Determine Whether the Equation Has Two two nonreal complex solutions \text { two nonreal complex solutions } two nonreal complex solutions

Use the Discriminant to Determine Whether the Equation Has Two $\text { two nonreal complex solutions }$