Solve for x: 2x^2 - 8x + 6 = 0.

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Question: Solve for x: 2x^2 - 8x + 6 = 0.

Options:

Correct Answer: 3

Solution:

Using the quadratic formula x = [8 ± √(64 - 48)] / 4 = [8 ± 4] / 4, giving x = 3 or x = 1.

Solve for x: 2x^2 - 8x + 6 = 0.

Solve for x: 2x^2 - 8x + 6 = 0.

Correct Answer: x = 3 or x = 1

Step 1: Identify the coefficients in the equation 2x^2 - 8x + 6 = 0. Here, a = 2, b = -8, and c = 6.
Step 2: Use the quadratic formula, which is x = [-b ± √(b² - 4ac)] / (2a).
Step 3: Calculate b² - 4ac. First, find b²: (-8)² = 64. Then calculate 4ac: 4 * 2 * 6 = 48. Now, subtract: 64 - 48 = 16.
Step 4: Substitute the values into the quadratic formula: x = [8 ± √16] / (2 * 2).
Step 5: Calculate √16, which is 4. Now the formula looks like this: x = [8 ± 4] / 4.
Step 6: Solve for the two possible values of x. First, calculate x = (8 + 4) / 4 = 12 / 4 = 3. Then calculate x = (8 - 4) / 4 = 4 / 4 = 1.
Step 7: The solutions are x = 3 and x = 1.

Quadratic Equations – The question tests the ability to solve quadratic equations using the quadratic formula.
Quadratic Formula – The quadratic formula is used to find the roots of a quadratic equation in the form ax^2 + bx + c = 0.
Discriminant – Understanding the discriminant (b^2 - 4ac) is crucial for determining the nature of the roots.