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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

User Uchitha
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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.

User Koya
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