Question

Solve each quadratic equation using the method of your choice. List each root in its own box or write prime in both if you cannot factor it. Express

any non-integers as fractions.
A. 2x2-17x+8=0
B. x² - 4x-12=0

Answer 1

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.