For the equation x^2 + 2x + 1 = 0, what is the nature of the roots?

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Question: For the equation x^2 + 2x + 1 = 0, what is the nature of the roots?

Options:

Correct Answer: Real and equal

Solution:

The discriminant is 2^2 - 4(1)(1) = 0, indicating that the roots are real and equal.

For the equation x^2 + 2x + 1 = 0, what is the nature of the roots?

For the equation x^2 + 2x + 1 = 0, what is the nature of the roots?

Step 1: Identify the coefficients in the equation x^2 + 2x + 1 = 0. Here, a = 1, b = 2, and c = 1.
Step 2: Use the formula for the discriminant, which is D = b^2 - 4ac.
Step 3: Substitute the values of a, b, and c into the discriminant formula: D = 2^2 - 4(1)(1).
Step 4: Calculate 2^2, which is 4.
Step 5: Calculate 4(1)(1), which is also 4.
Step 6: Now, subtract the two results: D = 4 - 4 = 0.
Step 7: Interpret the result. Since the discriminant D = 0, this means the roots of the equation are real and equal.

Quadratic Equations – Understanding the standard form of a quadratic equation and how to identify its coefficients.
Discriminant – Using the discriminant (b^2 - 4ac) to determine the nature of the roots of a quadratic equation.
Nature of Roots – Identifying whether the roots are real and distinct, real and equal, or complex based on the value of the discriminant.