What is the value of k if the roots of the equation x^2 + kx + 4 = 0 are -2 and

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Question: What is the value of k if the roots of the equation x^2 + kx + 4 = 0 are -2 and -2?

Options:

Correct Answer: 6

Solution:

The sum of the roots is -2 + -2 = -4, so k = 4.

What is the value of k if the roots of the equation x^2 + kx + 4 = 0 are -2 and -2?

What is the value of k if the roots of the equation x^2 + kx + 4 = 0 are -2 and -2?

Step 1: Identify the equation given, which is x^2 + kx + 4 = 0.
Step 2: Recognize that the roots of the equation are given as -2 and -2.
Step 3: Calculate the sum of the roots: -2 + -2 = -4.
Step 4: According to the formula for the sum of the roots in a quadratic equation, the sum is equal to -k. Therefore, -k = -4.
Step 5: Solve for k by multiplying both sides of the equation by -1: k = 4.

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