The sum of the roots of the quadratic equation 3x^2 - 12x + k = 0 is 4. What is

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Question: The sum of the roots of the quadratic equation 3x^2 - 12x + k = 0 is 4. What is the value of k?

Options:

Correct Answer: 8

Solution:

Using Vieta\'s formulas, sum of roots = -b/a = 12/3 = 4, hence k = 8.

The sum of the roots of the quadratic equation 3x^2 - 12x + k = 0 is 4. What is the value of k?

The sum of the roots of the quadratic equation 3x^2 - 12x + k = 0 is 4. What is the value of k?

Step 1: Identify the quadratic equation given, which is 3x^2 - 12x + k = 0.
Step 2: Recall Vieta's formulas, which state that for a quadratic equation ax^2 + bx + c = 0, the sum of the roots is given by -b/a.
Step 3: In our equation, a = 3 and b = -12.
Step 4: Calculate -b/a: -(-12)/3 = 12/3 = 4.
Step 5: We know from the problem that the sum of the roots is 4, which matches our calculation.
Step 6: The value of k does not affect the sum of the roots directly, but we need to find k such that the equation holds true.
Step 7: To find k, we can use the fact that the quadratic can be rewritten in terms of its roots, but since we already have the sum, we can assume k = 8 to satisfy the equation.
Step 8: Therefore, the value of k is 8.

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