The roots of the equation 2x^2 - 4x + 1 = 0 are:

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Question: The roots of the equation 2x^2 - 4x + 1 = 0 are:

Options:

Correct Answer: 1/2

Solution:

Using the quadratic formula, x = [4 ± √(16 - 8)] / 4 = [4 ± 2√2] / 4 = 1 ± √2/2. Hence, the roots are not simple fractions.

The roots of the equation 2x^2 - 4x + 1 = 0 are:

The roots of the equation 2x^2 - 4x + 1 = 0 are:

Step 1: Identify the coefficients in the quadratic equation 2x^2 - 4x + 1 = 0. Here, a = 2, b = -4, and c = 1.
Step 2: Write down the quadratic formula: x = [-b ± √(b² - 4ac)] / (2a).
Step 3: Substitute the values of a, b, and c into the formula. This gives us: x = [4 ± √((-4)² - 4 * 2 * 1)] / (2 * 2).
Step 4: Calculate b² - 4ac: (-4)² = 16 and 4 * 2 * 1 = 8. So, 16 - 8 = 8.
Step 5: Substitute this result back into the formula: x = [4 ± √8] / 4.
Step 6: Simplify √8. Since √8 = 2√2, we have: x = [4 ± 2√2] / 4.
Step 7: Split the fraction: x = 4/4 ± 2√2/4, which simplifies to x = 1 ± √2/2.
Step 8: Conclude that the roots of the equation are 1 + √2/2 and 1 - √2/2.

Quadratic Equations – Understanding how to solve quadratic equations using the quadratic formula.
Roots of Equations – Identifying and interpreting the roots of a quadratic equation.
Simplifying Expressions – Simplifying the results of the quadratic formula to find the roots.