Final answer:
The discriminant for the quadratic equation x² - 3x - 2 = 0 is calculated using the formula b² - 4ac. In this case, the discriminant is 17, which indicates that the equation has two distinct real roots.
Step-by-step explanation:
The discriminant in a quadratic equation of the form ax2 + bx + c = 0 is given by b2 - 4ac. It is used to determine the nature and number of the roots of the equation. For the given equation x2 - 3x - 2 = 0, the coefficients are a = 1, b = -3, and c = -2.
To compute the discriminant, we plug these values into the formula:
Discriminant = b2 - 4ac
= (-3)2 - 4(1)(-2)
= 9 - (-8)
= 9 + 8
= 17
Since the discriminant is positive and not a perfect square, the quadratic equation has two distinct real roots. These roots can be found by using the quadratic formula.