Solve x^2 -5x +6 =0.

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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 x^2 -5x +6 =0.

Explanation:
Factoring a quadratic with leading coefficient 1 relies on two numbers whose product is the constant term and whose sum is the middle coefficient. For x^2 - 5x + 6, we need a and b with ab = 6 and a + b = 5. The pair 2 and 3 fits both conditions, so the expression factors as (x - 2)(x - 3). Setting each factor to zero gives x = 2 or x = 3. Therefore, the solutions are x = 2 and x = 3. Other pairs wouldn’t multiply to 6 and sum to 5, so they don’t satisfy the equation.

Factoring a quadratic with leading coefficient 1 relies on two numbers whose product is the constant term and whose sum is the middle coefficient. For x^2 - 5x + 6, we need a and b with ab = 6 and a + b = 5. The pair 2 and 3 fits both conditions, so the expression factors as (x - 2)(x - 3). Setting each factor to zero gives x = 2 or x = 3. Therefore, the solutions are x = 2 and x = 3. Other pairs wouldn’t multiply to 6 and sum to 5, so they don’t satisfy the equation.

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