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.

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.

The quadratic equation you provided has

a = - 2 b = - 3 c = 8

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.