What is the value of the discriminant for the equation 3x^2 + 12x + 12 = 0?

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Question: What is the value of the discriminant for the equation 3x^2 + 12x + 12 = 0?

Options:

Correct Answer: 0

Solution:

The discriminant is b^2 - 4ac = 12^2 - 4(3)(12) = 144 - 144 = 0.

What is the value of the discriminant for the equation 3x^2 + 12x + 12 = 0?

What is the value of the discriminant for the equation 3x^2 + 12x + 12 = 0?

Step 1: Identify the coefficients a, b, and c from the equation 3x^2 + 12x + 12 = 0. Here, a = 3, b = 12, and c = 12.
Step 2: Write the formula for the discriminant, which is b^2 - 4ac.
Step 3: Calculate b^2. Since b = 12, we have 12^2 = 144.
Step 4: Calculate 4ac. Here, a = 3 and c = 12, so 4ac = 4 * 3 * 12.
Step 5: Calculate 4 * 3 = 12, then multiply by 12 to get 12 * 12 = 144.
Step 6: Now, substitute the values into the discriminant formula: 144 - 144.
Step 7: Perform the subtraction: 144 - 144 = 0.
Step 8: The value of the discriminant is 0.

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