Final answer:
To solve the quadratic equation 3x² - 12x + 13 = 0 using the quadratic formula, we find that a = 3, b = -12, and c = 13. Substituting these into the formula gives two complex solutions: x = 2 + i√2 and x = 2 - i√2.
Step-by-step explanation:
To solve the quadratic equation 3x² - 12x + 13 = 0 using the quadratic formula, we use the formula x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are coefficients from the equation ax² + bx + c = 0. In this case, a = 3, b = -12, and c = 13.
Substituting these values into the formula gives us:
x = (12 ± √((-12)² - 4 × 3 × 13)) / (2 × 3)
x = (12 ± √(144 - 156)) / 6
x = (12 ± √(-12)) / 6
Since the discriminant (the part under the square root) is negative, the solutions are complex numbers. So we have:
x = (12 ± √i√12) / 6
x = 2 ± i√12/6
x = 2 ± i√2
Therefore, the solutions of the quadratic equation in exact form are x = 2 + i√2 and x = 2 - i√2.