The sum of the roots of the quadratic equation 3x^2 + 12x + 12 = 0 is equal to w

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Question: The sum of the roots of the quadratic equation 3x^2 + 12x + 12 = 0 is equal to what? (2022)

Options:

Correct Answer: -4

Exam Year: 2022

Solution:

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

The sum of the roots of the quadratic equation 3x^2 + 12x + 12 = 0 is equal to what? (2022)

The sum of the roots of the quadratic equation 3x^2 + 12x + 12 = 0 is equal to what? (2022)

Step 1: Identify the coefficients of the quadratic equation 3x^2 + 12x + 12 = 0. Here, a = 3, b = 12, and c = 12.
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: Substitute the values of b and a into the formula. We have b = 12 and a = 3.
Step 4: Calculate -b/a. This means we calculate -12/3.
Step 5: Perform the division. -12 divided by 3 equals -4.
Step 6: Conclude that the sum of the roots of the quadratic equation is -4.

Vieta's Formulas – A mathematical theorem that relates the coefficients of a polynomial to sums and products of its roots.