The product of the roots of x^2 - 5x + 6 = 0 is equal to:

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Prepare for the CCC Common Core Pre-Test with our comprehensive quiz. Utilize detailed flashcards and multiple-choice questions, each accompanied by insights and explanations, to enhance your readiness for the exam!

Multiple Choice

The product of the roots of x^2 - 5x + 6 = 0 is equal to:

Explanation:
For a quadratic in standard form ax^2 + bx + c = 0, the product of its roots equals c divided by a. This comes from expanding (x − r1)(x − r2) = x^2 − (r1 + r2)x + r1r2, which shows the product of the roots is r1r2 = c/a. Here a = 1 and c = 6, so the product of the roots is 6/1 = 6. You can also see this by factoring the quadratic as (x − 2)(x − 3) = 0, whose roots are 2 and 3, and their product is 6. Therefore, the product of the roots is 6.

For a quadratic in standard form ax^2 + bx + c = 0, the product of its roots equals c divided by a. This comes from expanding (x − r1)(x − r2) = x^2 − (r1 + r2)x + r1r2, which shows the product of the roots is r1r2 = c/a.

Here a = 1 and c = 6, so the product of the roots is 6/1 = 6. You can also see this by factoring the quadratic as (x − 2)(x − 3) = 0, whose roots are 2 and 3, and their product is 6. Therefore, the product of the roots is 6.

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