A. To solve the quadratic equation 2x² - 17x + 8 = 0, we can use the factoring method. We need to find two numbers whose product is 16 (the product of the coefficients of x² and the constant term) and whose sum is -17 (the coefficient of x). These two numbers are -1 and -16, so we can rewrite the equation as:
2x² - 17x + 8 = (2x - 1)(x - 8) = 0
Setting each factor equal to zero, we get:
2x - 1 = 0 or x - 8 = 0
Solving for x, we get:
2x = 1 or x = 8
x = 1/2 or x = 8
Therefore, the roots of the quadratic equation are x = 1/2 and x = 8.
B. To solve the quadratic equation x² - 4x - 12 = 0, we can use the factoring method. We need to find two numbers whose product is -12 (the product of the coefficients of x² and the constant term) and whose sum is -4 (the coefficient of x). These two numbers are -6 and 2, so we can rewrite the equation as:
x² - 4x - 12 = (x - 6)(x + 2) = 0
Setting each factor equal to zero, we get:
x - 6 = 0 or x + 2 = 0
Solving for x, we get:
x = 6 or x = -2
Therefore, the roots of the quadratic equation are x = 6 and x = -2.