Answer: The sum of the cubes of the roots of a quadratic equation with coefficients a, b, and c can be found using the formula:
x³ + y³ = (x + y)(x² - xy + y²) = -b
Where x and y are the roots of the equation ax² + bx + c = 0.
In this case, the equation is 2x² - 10x + 12 = 0, so a = 2, b = -10, and c = 12.
So, the sum of the cubes of the roots is:
x³ + y³ = -b = -(-10) = 10
Therefore, the sum of the cubes of the roots of the equation 2x² - 10x + 12 = 0 is 10.
Explanation: