If the quadratic equation x^2 + 4x + 4 = 0 is solved, what is the nature of its

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Question: If the quadratic equation x^2 + 4x + 4 = 0 is solved, what is the nature of its roots? (2019)

Options:

Correct Answer: One real root

Exam Year: 2019

Solution:

The discriminant is 0, indicating one real root (a repeated root).

If the quadratic equation x^2 + 4x + 4 = 0 is solved, what is the nature of its roots? (2019)

If the quadratic equation x^2 + 4x + 4 = 0 is solved, what is the nature of its roots? (2019)

Step 1: Identify the quadratic equation, which is x^2 + 4x + 4 = 0.
Step 2: Recognize the standard form of a quadratic equation, which is ax^2 + bx + c = 0.
Step 3: Identify the coefficients: a = 1, b = 4, c = 4.
Step 4: Calculate the discriminant using the formula D = b^2 - 4ac.
Step 5: Substitute the values into the discriminant formula: D = (4)^2 - 4(1)(4).
Step 6: Simplify the calculation: D = 16 - 16 = 0.
Step 7: Interpret the result: Since the discriminant D = 0, it means there is one real root.
Step 8: Conclude that the nature of the roots is one repeated real root.

Quadratic Equations – Understanding the standard form of a quadratic equation and how to identify its roots using the discriminant.
Discriminant – The discriminant (b^2 - 4ac) determines the nature of the roots of a quadratic equation: two distinct real roots, one repeated real root, or two complex roots.