For x^2 - 5x + 6 = 0, the sum of the roots is?

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Multiple Choice

For x^2 - 5x + 6 = 0, the sum of the roots is?

Explanation:
Think about how the roots relate to the coefficients. For a quadratic ax^2 + bx + c = 0, the sum of the roots equals -b/a. This comes from Viète’s formulas, and it holds whether you factor or use the quadratic formula. Here, a = 1 and b = -5, so the sum of the roots is -(-5)/1 = 5. You can also see it by factoring: x^2 - 5x + 6 factors as (x - 2)(x - 3), giving roots 2 and 3, whose sum is 5. The other numbers don’t match the sum here: 6 is the product of the roots (2 × 3), not their sum; 0 isn’t possible since x = 0 gives 6 ≠ 0; -5 is the coefficient with opposite sign, not the sum.

Think about how the roots relate to the coefficients. For a quadratic ax^2 + bx + c = 0, the sum of the roots equals -b/a. This comes from Viète’s formulas, and it holds whether you factor or use the quadratic formula. Here, a = 1 and b = -5, so the sum of the roots is -(-5)/1 = 5.

You can also see it by factoring: x^2 - 5x + 6 factors as (x - 2)(x - 3), giving roots 2 and 3, whose sum is 5.

The other numbers don’t match the sum here: 6 is the product of the roots (2 × 3), not their sum; 0 isn’t possible since x = 0 gives 6 ≠ 0; -5 is the coefficient with opposite sign, not the sum.

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