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.
-$\text { one real solution with a multiplicity of two }$
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.
-$\text { one real solution with a multiplicity of two }$ 
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

The discriminant of a quadratic equation $ax^2 + bx + c = 0$ is given by $b^2 - 4ac$. For one real solution with a multiplicity of two, the discriminant must be zero. For option B, the discriminant is $12^2 - 4(4)(9) = 144 - 144 = 0$, indicating one real solution with a multiplicity of two.

Use the Discriminant to Determine Whether the Equation Has Two one real solution with a multiplicity of two \text { one real solution with a multiplicity of two } one real solution with a multiplicity of two

Use the Discriminant to Determine Whether the Equation Has Two $\text { one real solution with a multiplicity of two }$