The quadratic equation x² + 4x + 4 = 0 has how many distinct roots? (2021)

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Question: The quadratic equation x² + 4x + 4 = 0 has how many distinct roots? (2021)

Options:

Correct Answer: 1

Exam Year: 2021

Solution:

The discriminant is 4² - 4*1*4 = 0, indicating one distinct root.

The quadratic equation x² + 4x + 4 = 0 has how many distinct roots? (2021)

The quadratic equation x² + 4x + 4 = 0 has how many distinct roots? (2021)

Step 1: Identify the coefficients of the quadratic equation x² + 4x + 4 = 0. Here, a = 1, b = 4, and c = 4.
Step 2: Use the formula for the discriminant, which is D = b² - 4ac.
Step 3: Substitute the values of a, b, and c into the discriminant formula: D = 4² - 4*1*4.
Step 4: Calculate 4², which is 16.
Step 5: Calculate 4*1*4, which is 16.
Step 6: Now, subtract the two results: D = 16 - 16 = 0.
Step 7: Interpret the result: A discriminant of 0 means there is one distinct root.

Quadratic Equations – Understanding the standard form of a quadratic equation and how to determine the number of roots using the discriminant.
Discriminant – The formula b² - 4ac is used to determine the nature of the roots of a quadratic equation.