Find the roots of the equation 6p2 - 5p - 6 = 0.

Explanation

To find the roots of the quadratic equation: 6p2 - 5p - 6 = 0 we use the quadratic formula: p = (-b ± √(b2 - 4ac)) / 2a where a = 6, b = -5, and c = -6. Step 1: Substitute values into the formula p = (-(-5) ± √((-5)2 - 4 * 6 * (-6))) / (2 * 6) p = (5 ± √(25 + 144)) / 12 p = (5 ± √169) / 12 Step 2: Simplify the square root p = (5 ± 13) / 12 Step 3: Solve for both roots 1. For the positive case: p = (5 + 13) / 12 = 18 / 12 = 3 / 2 2. For the negative case: p = (5 - 13) / 12 = -8 / 12 = -2 / 3 Final Answer The roots of the equation 6p2 - 5p - 6 = 0 are: p = 3 / 2 and p = -2 / 3