Find the x-intercepts of the equation 3x^2 + 12x + 12 = 0.

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Question: Find the x-intercepts of the equation 3x^2 + 12x + 12 = 0.

Options:

Correct Answer: x = -4

Solution:

Using the quadratic formula: a = 3, b = 12, c = 12. Discriminant = 12² - 4(3)(12) = 144 - 144 = 0. x = -b / 2a = -12 / 6 = -2.

Find the x-intercepts of the equation 3x^2 + 12x + 12 = 0.

Find the x-intercepts of the equation 3x^2 + 12x + 12 = 0.

Step 1: Identify the equation you need to solve, which is 3x^2 + 12x + 12 = 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 = 12.
Step 3: Calculate the discriminant using the formula: Discriminant = b² - 4ac.
Step 4: Substitute the values of a, b, and c into the discriminant formula: Discriminant = 12² - 4(3)(12).
Step 5: Calculate 12², which is 144.
Step 6: Calculate 4(3)(12), which is 144.
Step 7: Subtract the two results: 144 - 144 = 0.
Step 8: Since the discriminant is 0, there is one real solution for x.
Step 9: Use the quadratic formula to find x: x = -b / (2a).
Step 10: Substitute b and a into the formula: x = -12 / (2 * 3).
Step 11: Calculate 2 * 3, which is 6.
Step 12: Now divide -12 by 6: x = -12 / 6 = -2.
Step 13: The x-intercept of the equation is x = -2.

Quadratic Equations – Understanding how to solve quadratic equations using the quadratic formula and identifying x-intercepts.
Discriminant – Using the discriminant to determine the nature of the roots of a quadratic equation.