Final answer:
The given quadratic equation 3x² - 10 = 0 has a positive discriminant of 120, indicating it has two distinct real and irrational roots.
Step-by-step explanation:
To determine the nature of the roots of a quadratic equation, we can use the discriminant, which is the part of the quadratic formula under the square root sign (√). The general form of the quadratic equation is ax² + bx + c = 0, and the discriminant is b² - 4ac. For the given equation 3x² - 10 = 0, which is already in standard form, the coefficients are a = 3, b = 0, and c = -10.
Calculating the discriminant gives us: (0)² - 4(3)(-10) = 0 + 120 = 120. Since the discriminant is positive, this means the equation has two distinct real roots. Furthermore, because the discriminant is a perfect square (11² = 121 is close but not equal to 120), the roots are real and irrational.