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

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Multiple Choice

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

Explanation:
For a quadratic in standard form ax^2 + bx + c = 0, the product of the roots equals c divided by a. This comes from writing the quadratic as a(x − r1)(x − r2), which expands to a[x^2 − (r1 + r2)x + r1r2], so the constant term c equals a·r1r2 and thus r1r2 = c/a. Here, a = 3 and c = 9, so the product of the roots is 9/3 = 3. A quick check by factoring: 3x^2 − 12x + 9 = 3(x^2 − 4x + 3) = 3(x − 1)(x − 3), giving roots 1 and 3, whose product is 3.

For a quadratic in standard form ax^2 + bx + c = 0, the product of the roots equals c divided by a. This comes from writing the quadratic as a(x − r1)(x − r2), which expands to a[x^2 − (r1 + r2)x + r1r2], so the constant term c equals a·r1r2 and thus r1r2 = c/a.

Here, a = 3 and c = 9, so the product of the roots is 9/3 = 3. A quick check by factoring: 3x^2 − 12x + 9 = 3(x^2 − 4x + 3) = 3(x − 1)(x − 3), giving roots 1 and 3, whose product is 3.

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