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

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Question: What is the sum of the roots of the equation 3x^2 - 12x + 9 = 0?

Options:

Correct Answer: 4

Solution:

Using Vieta\'s formulas, the sum of the roots is -(-12)/3 = 4.

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

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

Step 1: Identify the equation given, which is 3x^2 - 12x + 9 = 0.
Step 2: Recognize that this is a quadratic equation in the form ax^2 + bx + c = 0, where a = 3, b = -12, and c = 9.
Step 3: Use Vieta's formulas, which tell us that the sum of the roots of the equation is given by -b/a.
Step 4: Substitute the values of b and a into the formula: -(-12)/3.
Step 5: Simplify the expression: -(-12) equals 12, so we have 12/3.
Step 6: Calculate 12 divided by 3, which equals 4.
Step 7: Conclude that the sum of the roots of the equation is 4.

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