Final answer:
The discriminant of the quadratic expression 2x² + 5x - 2 is calculated using the formula b² - 4ac, resulting in a value of 41, which indicates two distinct real roots.
Step-by-step explanation:
To calculate the discriminant of the quadratic expression 2x² + 5x - 2, we use the formula for the discriminant, which is given by b² - 4ac, where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0. For the given quadratic expression, a = 2, b = 5, and c = -2.
Plugging these values into the discriminant formula, we get:
Discriminant = b² - 4ac = (5) ² - 4(2)(-2) = 25 + 16 = 41.
Since the discriminant is positive, this indicates that the quadratic equation has two distinct real roots.