What is the discriminant of the quadratic equation: 2x ^ 2 – 5x + 3 = 0.

The given equation 2x ^ 2 – 5x + 3 = 0 is a complete quadratic equation of the form ax ^ 2 + bx + c = 0.

To find the discriminant of the equation, we apply the formula:

D = b ^ 2 – 4ac;

We write out the coefficients of the equation and calculate the discriminant.

a = 2; b = -5; c = 3;

Substitute the values into the formula:

D = (-5) ^ 2 – 4 * 2 * 6 = 25 – 24 = 1.

The discriminant is greater than zero – the equation has two roots.

x1 = (-b + √D) / 2a = (- (- 5) + √1) / 2 * 2 = (5 + 1) / 4 = 6/4 = 1.5;

x2 = (-b – √D) / 2a = (- (- 5) – √1) / 2 * 2 = (5 – 1) / 4 = 4/4 = 1.