What are the roots of x 2 + 8x – 48 = 0?

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The roots of a quadratic are the solutions of the quadratic. Factor the quadratic and set each factor equal to 0 to find the roots. To find the factors of a quadratic, begin by finding two numbers whose product is equal to the constant of the quadratic. Of those numbers, find the pair that adds to the coefficient of the x term of the quadratic; –4 and 12 multiply to –48 and add to 8. Therefore, the factors of x 2 + 8x – 48 are (x – 4) and (x + 12). Set each factor equal to 0 and solve for x: x – 4 = 0, x = 4, and x + 12 = 0, x = –12. The roots of x 2 + 8x – 48 are 4 and –12.

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