Which of the following are the solutions to the equation \(x^{2}-7 x+12=0\)?

A. x = 3 and x = 4

Explanation

Factor the equation. What two numbers have a sum of –7 and a product of 12. The factors of 12 are 1 and 12, 2 and 6, and 3 and 4. The factors 3 and 4 have a sum of 7. Since 7 is negative, the factors must both be negative, so the equation factors to \((x-3)(x-4)=0\). Set both factors equal to 0. If x – 3 = 0, then add three to both sides to get x = 3. If x – 4 = 0, add four to both sides to get x = 4. The correct answer is (A).

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