What is the value of k if the roots of the equation x^2 + kx + 16 = 0 are equal?

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Question: What is the value of k if the roots of the equation x^2 + kx + 16 = 0 are equal?

Options:

Correct Answer: 8

Solution:

For equal roots, the discriminant must be zero: k^2 - 4*1*16 = 0 => k^2 = 64 => k = 8 or k = -8.

What is the value of k if the roots of the equation x^2 + kx + 16 = 0 are equal?

What is the value of k if the roots of the equation x^2 + kx + 16 = 0 are equal?

Step 1: Identify the equation given, which is x^2 + kx + 16 = 0.
Step 2: Understand that for the roots of a quadratic equation to be equal, the discriminant must be zero.
Step 3: Write down the formula for the discriminant, which is D = b^2 - 4ac. Here, a = 1, b = k, and c = 16.
Step 4: Substitute the values into the discriminant formula: D = k^2 - 4*1*16.
Step 5: Simplify the expression: D = k^2 - 64.
Step 6: Set the discriminant equal to zero for equal roots: k^2 - 64 = 0.
Step 7: Solve for k by adding 64 to both sides: k^2 = 64.
Step 8: Take the square root of both sides: k = 8 or k = -8.

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