Find the roots of the quadratic equation x^2 - 7x + 12 = 0.
Answer and explanation
Correct answer: D. x = 3 and x = 4
- Step 1: Factorize the quadratic expression: find two numbers with sum -7 and product 12 (-3 and -4). Step 2. Equation factors as (x - 3)(x - 4) = 0, giving solutions x = 3 and x = 4. Answer: x = 3 and x = 4. Why not the others: x = -3 and x = -4 gives x^2 + 7x + 12 = 0; x = 2 and x = 6 gives sum 8; x = -2 and x = -6 gives sum -8.
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