Solve 2x^2 - 5x + 3 = 0. Which of the following are the real solutions?

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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 2x^2 - 5x + 3 = 0. Which of the following are the real solutions?

Explanation:
When solving a quadratic by factoring, you use the zero-product property: if a product is zero, each factor can be zero. For 2x^2 - 5x + 3, find two numbers that multiply to (2)(3) = 6 and add to -5. Those numbers are -2 and -3. Rewrite and factor: 2x^2 - 5x + 3 = 2x^2 - 2x - 3x + 3 = 2x(x - 1) - 3(x - 1) = (2x - 3)(x - 1). Set each factor to zero and solve: 2x - 3 = 0 gives x = 3/2, and x - 1 = 0 gives x = 1. So the real solutions are x = 1 and x = 3/2.

When solving a quadratic by factoring, you use the zero-product property: if a product is zero, each factor can be zero. For 2x^2 - 5x + 3, find two numbers that multiply to (2)(3) = 6 and add to -5. Those numbers are -2 and -3. Rewrite and factor: 2x^2 - 5x + 3 = 2x^2 - 2x - 3x + 3 = 2x(x - 1) - 3(x - 1) = (2x - 3)(x - 1). Set each factor to zero and solve: 2x - 3 = 0 gives x = 3/2, and x - 1 = 0 gives x = 1. So the real solutions are x = 1 and x = 3/2.

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