Question

Solve 3x² + 17x - 6 = 0.

Based on the work shown above, which of these values are possible solutions of the equation? Check all of the boxes that apply.

A. x = -6
B. x = 6
C. x = -⅓
D. x = ⅓
E. x = 0

Answer 1

The quadratic equation 3x² + 17x - 6 = 0 is solved using the quadratic formula. The possible solutions are x = 1/3 and x = −6, which correspond to options A and D respectively.

Step-by-step explanation:

To solve the quadratic equation 3x² + 17x - 6 = 0, you can use the quadratic formula which is given by:

x = −b ± √(b² - 4ac) / (2a)

Here, a = 3, b = 17, and c = −6. Plugging these values into the quadratic formula:

x = −17 ± √(17² - 4 × 3 × (−6)) / (2 × 3)

x = −17 ± √(289 + 72) / 6

x = −17 ± √361 / 6

x = −17 ± 19 / 6

This gives us two possible solutions for x:

• x = (−17 + 19) / 6 = 2 / 6 = 1/3, which confirms option D.
• x = (−17 − 19) / 6 = −36 / 6 = −6, which confirms option A.

Hence, the possible solutions to the equation are x = 1/3 and x = −6.