What is the value of the discriminant b^2-4ac for the quatrain equation 0=-2x^2-3x+8, and what does it mean about the number of real solutions the equation has.

The quadratic equation you provided has

so the discriminant b²-4ac is ...

... b² - 4ac = (-3)² -4(-2)(8) = 9 + 64 = 73

The discriminant is positive, so there are two real solutions to the given equation.

Answer

discriminant = 73

The discriminant determines whether the equation has real root or it has imaginary roots. The equation has 2 real solutions

Explanation

0=-2x²-3x+8  ⇒ -2x² -3x + 8 = 0

Now the equation resembles the general quadratic formula ax² + bx + c = 0

The discriminant is b^2-4ac = (-3)² -(4 × -2 × 8)

                                                  =  9 + 64

                                                  = 73

The discriminant determines whether the equation has real root or it has imaginary roots. When b^2-4ac is equal to positive number the equation has a real roots or solutions, when negative, then the solutions are imaginary numbers.