Final answer:
The discriminant of the quadratic equation 3x² - 10x + 2 is found using the formula b² - 4ac, which equals 76, indicating two distinct real roots. The correct answer is option a. 76
Step-by-step explanation:
To find the discriminant of a quadratic equation in the form ax² + bx + c = 0, you use the formula b² - 4ac. The discriminant helps determine the nature of the roots of the quadratic equation - whether they are real or complex, and whether they are distinct or repeated.
For the quadratic equation 3x² - 10x + 2 = 0 (after correcting the initial minus sign to a plus to make mathematical sense of the equation), we have values a = 3, b = -10, and c = 2. Plugging these into the discriminant formula, we get:
(-10)² - 4 × 3 × 2 = 100 - 24 = 76.
Therefore, the discriminant of the equation 3x² - 10x + 2 is 76, which indicates the equation has two distinct real roots.