What is the value of the discriminant for the quadratic equation 3x^2 + 12x + 9

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Question: What is the value of the discriminant for the quadratic equation 3x^2 + 12x + 9 = 0? (2019)

Options:

Correct Answer: 0

Exam Year: 2019

Solution:

The discriminant D = b^2 - 4ac = 12^2 - 4*3*9 = 0, indicating equal roots.

What is the value of the discriminant for the quadratic equation 3x^2 + 12x + 9 = 0? (2019)

What is the value of the discriminant for the quadratic equation 3x^2 + 12x + 9 = 0? (2019)

Step 1: Identify the coefficients a, b, and c from the quadratic equation 3x^2 + 12x + 9 = 0. Here, a = 3, b = 12, and c = 9.
Step 2: Use the formula for the discriminant, which is D = 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 = 9, so 4 * 3 * 9 = 108.
Step 5: Substitute the values into the discriminant formula: D = 144 - 108.
Step 6: Perform the subtraction: 144 - 108 = 36.
Step 7: The value of the discriminant D is 36.

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