If the quadratic equation x^2 + 2x + 1 = 0 is solved, what is the nature of the

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Question: If the quadratic equation x^2 + 2x + 1 = 0 is solved, what is the nature of the roots? (2022)

Options:

Correct Answer: Real and equal

Exam Year: 2022

Solution:

The discriminant is 0, indicating that the roots are real and equal.

If the quadratic equation x^2 + 2x + 1 = 0 is solved, what is the nature of the roots? (2022)

If the quadratic equation x^2 + 2x + 1 = 0 is solved, what is the nature of the roots? (2022)

Step 1: Identify the quadratic equation, which is x^2 + 2x + 1 = 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 = 2, c = 1.
Step 4: Calculate the discriminant using the formula D = b^2 - 4ac.
Step 5: Substitute the values into the discriminant formula: D = (2)^2 - 4(1)(1).
Step 6: Simplify the calculation: D = 4 - 4 = 0.
Step 7: Analyze the value of the discriminant: Since D = 0, it indicates that the roots are real and equal.

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: real and distinct, real and equal, or complex.