Question

Solve the equation by using the quadratic formula. 3x² - 1 = 7x. Select the best answer from the choices provided.

1) (7 + √37)/6
2) (7 - √37)/6
3) (-7 + √37)/6
4) (-7 - √37)/6

Answer 1

The equation 3x² - 7x + 1 = 0 is solved using the quadratic formula, giving solutions (7 + √37) / 6 and (7 - √37) / 6, corresponding to choices 1 and 2 provided.

Step-by-step explanation:

To solve the quadratic equation 3x² - 7x + 1 = 0 using the quadratic formula, we first identify the coefficients: a = 3, b = -7, and c = 1. The quadratic formula is given by x = (-b ± √(b² - 4ac)) / (2a). Substituting our values into the formula, we get:

x = (-(-7) ± √((-7)² - 4 × 3 × 1)) / (2 × 3)

x = (7 ± √(49 - 12)) / 6

x = (7 ± √(37)) / 6

Therefore, the solutions are (7 + √37) / 6 and (7 - √37) / 6, which correspond to choices 1 and 2 provided by the student.