The equation x^2 - 2x + 1 = 0 has how many distinct roots?

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Question: The equation x^2 - 2x + 1 = 0 has how many distinct roots?

Options:

Correct Answer: 1

Solution:

The discriminant is 0, indicating that there is exactly one distinct root.

The equation x^2 - 2x + 1 = 0 has how many distinct roots?

The equation x^2 - 2x + 1 = 0 has how many distinct roots?

Step 1: Identify the equation given, which is x^2 - 2x + 1 = 0.
Step 2: Recognize that this is a quadratic equation in the form ax^2 + bx + c.
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 formula: D = (-2)^2 - 4(1)(1).
Step 6: Simplify the calculation: D = 4 - 4 = 0.
Step 7: Interpret the result: A discriminant of 0 means there is exactly 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 discriminant (b^2 - 4ac) helps determine the nature of the roots of a quadratic equation.