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

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Multiple Choice

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

Explanation:
For any quadratic in standard form ax^2 + bx + c = 0, the sum of the roots is -b/a. This comes from Vieta’s formulas and tells us how the coefficients relate to the roots. Here, a = 3 and b = -12. The sum of the roots is -(-12)/3 = 12/3 = 4. You can also see this by factoring: 3x^2 - 12x + 9 = 3(x^2 - 4x + 3) = 3(x - 1)(x - 3). The roots are 1 and 3, which add up to 4. So the sum of the roots is 4.

For any quadratic in standard form ax^2 + bx + c = 0, the sum of the roots is -b/a. This comes from Vieta’s formulas and tells us how the coefficients relate to the roots.

Here, a = 3 and b = -12. The sum of the roots is -(-12)/3 = 12/3 = 4.

You can also see this by factoring: 3x^2 - 12x + 9 = 3(x^2 - 4x + 3) = 3(x - 1)(x - 3). The roots are 1 and 3, which add up to 4. So the sum of the roots is 4.

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