Question

The roots of the equation \( x^2 - 2x + 1 = 0 \) will be:

• A. 1, 1
• B. 1, -1
• C. 2, -2
• D. 2, 2

Hint:

For a perfect square trinomial like \( x^2 - 2x + 1 \), the root is repeated and can be found by factoring the trinomial.

Answer 1

The Correct Option is A

Step 1: Write the given equation.
We are given the quadratic equation: \[ x^2 - 2x + 1 = 0 \]
Step 2: Factor the quadratic equation.
This is a perfect square trinomial: \[ (x - 1)^2 = 0 \]
Step 3: Solve for \( x \).
Taking the square root of both sides: \[ x - 1 = 0 \quad \Rightarrow \quad x = 1 \] Thus, the roots of the equation are \( x = 1 \) and \( x = 1 \).
Step 4: Conclusion.
The roots of the equation are 1 and 1. Therefore, the correct answer is (A).