The roots of the equation x² - 8x + k = 0 are 4 and 4. Find k. (2021)

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Question: The roots of the equation x² - 8x + k = 0 are 4 and 4. Find k. (2021)

Options:

Correct Answer: 16

Exam Year: 2021

Solution:

Using the product of roots: k = 4 * 4 = 16.

The roots of the equation x² - 8x + k = 0 are 4 and 4. Find k. (2021)

The roots of the equation x² - 8x + k = 0 are 4 and 4. Find k. (2021)

Step 1: Identify the given quadratic equation, which is x² - 8x + k = 0.
Step 2: Note that the roots of the equation are given as 4 and 4 (which means both roots are the same).
Step 3: Recall the relationship between the roots and the constant term (k) in a quadratic equation. The product of the roots can be used to find k.
Step 4: Calculate the product of the roots: 4 * 4.
Step 5: Perform the multiplication: 4 * 4 = 16.
Step 6: Conclude that k = 16.

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