Final answer:
The discriminant for the equation 2x² - 3x + 10 = 0 is -71. The equation has two complex roots.
Step-by-step explanation:
The discriminant for the equation 2x² - 3x + 10 = 0 is calculated using the formula:
discriminant = b² - 4ac
Plug in the values from the equation:
a = 2, b = -3, c = 10
discriminant = (-3)² - 4(2)(10)
discriminant = 9 - 80
discriminant = -71
The discriminant is -71. Since the discriminant is negative, the equation has two complex roots that are conjugate pairs, which means they cannot be expressed as real numbers.