Question

Which statement is true about this quadratic equation? y= -2x2+9x-12

a.There are two complex solutions.
b.There is one real solution.
c.There is one complex solution.
d.There are two real solutions.

Answer 1

The quadratic equation y = -2x^2 + 9x - 12 has two complex solutions.

Step-by-step explanation:

The quadratic equation given is y = -2x^2 + 9x - 12. To determine the number of solutions, we can analyze the discriminant, which is the expression under the square root in the quadratic formula. The discriminant is calculated as b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation.

In this case, a = -2, b = 9, and c = -12. Let's substitute these values into the discriminant:

Discriminant = 9^2 - 4(-2)(-12) = 81 - 96 = -15.

Since the discriminant is negative (-15), the quadratic equation has two complex solutions. Therefore, the correct answer is option a. There are two complex solutions.