The roots of the quadratic equation x^2 - 4x + k = 0 are 2 and 2. What is the va

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Question: The roots of the quadratic equation x^2 - 4x + k = 0 are 2 and 2. What is the value of k? (2022)

Options:

Correct Answer: 4

Exam Year: 2022

Solution:

If the roots are both 2, then k = 2^2 - 4*2 = 4 - 8 = -4. Thus, k = 4.

The roots of the quadratic equation x^2 - 4x + k = 0 are 2 and 2. What is the value of k? (2022)

The roots of the quadratic equation x^2 - 4x + k = 0 are 2 and 2. What is the value of k? (2022)

Step 1: Identify the quadratic equation given, which is x^2 - 4x + k = 0.
Step 2: Note that the roots of the equation are both 2.
Step 3: Use the formula for a quadratic equation, which is x^2 - (sum of roots)x + (product of roots) = 0.
Step 4: Since both roots are 2, the sum of the roots is 2 + 2 = 4.
Step 5: The product of the roots is 2 * 2 = 4.
Step 6: Rewrite the quadratic equation using the sum and product of the roots: x^2 - 4x + (product of roots) = 0.
Step 7: Substitute the product of the roots (which is 4) into the equation: x^2 - 4x + 4 = 0.
Step 8: Compare this with the original equation x^2 - 4x + k = 0 to find k.
Step 9: Since the equations are the same, we find that k = 4.

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