Solve the equation 3x^2 - 12x + 9 = 0. Which are the correct solutions for x?

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Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

Solve the equation 3x^2 - 12x + 9 = 0. Which are the correct solutions for x?

Explanation:
Factoring a quadratic and using the zero-product property is the key idea here. Start by factoring out the common factor: 3x^2 - 12x + 9 = 3(x^2 - 4x + 3). Then factor the quadratic inside: x^2 - 4x + 3 = (x - 1)(x - 3). So the equation becomes 3(x - 1)(x - 3) = 0. By the zero-product property, either x - 1 = 0 or x - 3 = 0, giving x = 1 or x = 3. You can verify by substitution: x = 1 or x = 3 both satisfy the original equation. The other values don’t work because substituting them does not yield zero.

Factoring a quadratic and using the zero-product property is the key idea here. Start by factoring out the common factor: 3x^2 - 12x + 9 = 3(x^2 - 4x + 3). Then factor the quadratic inside: x^2 - 4x + 3 = (x - 1)(x - 3). So the equation becomes 3(x - 1)(x - 3) = 0. By the zero-product property, either x - 1 = 0 or x - 3 = 0, giving x = 1 or x = 3. You can verify by substitution: x = 1 or x = 3 both satisfy the original equation. The other values don’t work because substituting them does not yield zero.

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