For the following equation, state the value of the discriminant and then describe the

nature of the solutions. -9x^2+6x-2=0 what is the value of the discriminant? Which one
of the statements below is correct? A) the equation has two imaginary solutions. B) the
equation has two real solutions. C) the equation has one real solution

I have this has two real solutions and the discriminant is 49

Is this correct?

There is no need for an equation to ever start with a negative term, we can just multiply each term by -1 (just switch the signs)

-9x^2 + 6x - 2 = 0
9x^2 - 6x + 2 = 0

discr. = b^2 - 4ac = 36 - 4(9)(2) = -36

so there are two imaginary solutions.

No, your answer is not correct. Let me explain how to determine the value of the discriminant and the nature of the solutions for the given equation.

The discriminant (denoted as Δ) is a value calculated using the coefficients of the quadratic equation, specifically for equations of the form ax^2 + bx + c = 0. It helps determine the nature of the solutions.

In this case, the given quadratic equation is -9x^2 + 6x - 2 = 0. To determine the value of the discriminant, we need to use the formula: Δ = b^2 - 4ac.

From the equation, we have:
a = -9, b = 6, and c = -2.

Substituting these values into the formula, we have:
Δ = (6)^2 - 4(-9)(-2)
= 36 - 72
= -36.

The value of the discriminant is -36, not 49 as you mentioned. Now, we can determine the nature of the solutions based on the value of the discriminant.

If Δ > 0, then the equation has two distinct real solutions.
If Δ = 0, then the equation has one real solution (a repeated root).
If Δ < 0, then the equation has two imaginary solutions (complex roots).

In this case, since Δ = -36, which is less than 0, the correct statement is:
A) the equation has two imaginary solutions.

Therefore, the correct answer is: The equation has two imaginary solutions, and the value of the discriminant is -36.