The numbers a and b satisfy a+b=7 and ab=12. What are the numbers?

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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

The numbers a and b satisfy a+b=7 and ab=12. What are the numbers?

Explanation:
When two numbers have a specified sum and product, they are the roots of the quadratic x^2 − (sum)x + product = 0. Here the sum is 7 and the product is 12, giving x^2 − 7x + 12 = 0. This factors as (x − 3)(x − 4) = 0, so x = 3 or x = 4. The two numbers are 3 and 4 (order doesn’t matter). Quick check: 3 + 4 = 7 and 3 × 4 = 12. The other pairs don’t satisfy both conditions.

When two numbers have a specified sum and product, they are the roots of the quadratic x^2 − (sum)x + product = 0. Here the sum is 7 and the product is 12, giving x^2 − 7x + 12 = 0. This factors as (x − 3)(x − 4) = 0, so x = 3 or x = 4. The two numbers are 3 and 4 (order doesn’t matter). Quick check: 3 + 4 = 7 and 3 × 4 = 12. The other pairs don’t satisfy both conditions.

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