For the quadratic 3x^2 - 12x + 9 = 0, what is the product of its roots?

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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

For the quadratic 3x^2 - 12x + 9 = 0, what is the product of its roots?

Explanation:
The product of the roots of a quadratic ax^2 + bx + c = 0 is c divided by a (as long as a ≠ 0). Here the quadratic is 3x^2 - 12x + 9, so a = 3 and c = 9. The product is 9/3 = 3. You can also see this by factoring: 3x^2 - 12x + 9 = 3(x^2 - 4x + 3) = 3(x - 1)(x - 3), whose roots are 1 and 3, whose product is 3. The other values (0, 9, 1) don’t match the actual product.

The product of the roots of a quadratic ax^2 + bx + c = 0 is c divided by a (as long as a ≠ 0). Here the quadratic is 3x^2 - 12x + 9, so a = 3 and c = 9. The product is 9/3 = 3.

You can also see this by factoring: 3x^2 - 12x + 9 = 3(x^2 - 4x + 3) = 3(x - 1)(x - 3), whose roots are 1 and 3, whose product is 3. The other values (0, 9, 1) don’t match the actual product.

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