What is the value of k for which the equation x² - 6x + k = 0 has roots 2 and 4?

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Question: What is the value of k for which the equation x² - 6x + k = 0 has roots 2 and 4? (2022)

Options:

Correct Answer: 12

Exam Year: 2022

Solution:

The product of the roots is k = 2 * 4 = 8.

What is the value of k for which the equation x² - 6x + k = 0 has roots 2 and 4? (2022)

What is the value of k for which the equation x² - 6x + k = 0 has roots 2 and 4? (2022)

Step 1: Identify the roots of the equation. The roots given are 2 and 4.
Step 2: Recall that for a quadratic equation in the form x² - (sum of roots)x + (product of roots) = 0, the product of the roots is equal to k.
Step 3: Calculate the product of the roots. Multiply the roots: 2 * 4.
Step 4: Perform the multiplication: 2 * 4 = 8.
Step 5: Conclude that the value of k is 8.

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