Question

select the correct answer.
which statement is true about this quadratic equation?
y = -2x² + 9x - 12
a. there are two complex solutions.
b. there are two real solutions.
c. there is one complex solution.
d. there is one real solution.

Explanation:

Step1: Recall discriminant formula

For quadratic equation \(ax^2 + bx + c = 0\), discriminant \(D = b^2 - 4ac\).
Here, \(a=-2\), \(b = 9\), \(c=-12\).

Step2: Calculate discriminant

\(D=(9)^2 - 4\times(-2)\times(-12)\)
\(= 81-96\)
\(=-15\)

Step3: Analyze discriminant

Since \(D=-15<0\), the quadratic equation has two complex solutions (because complex solutions occur when discriminant is negative, and for quadratics, they come in conjugate pairs).

Answer:

A. There are two complex solutions.