What is the value of k if the equation x^2 + kx + 16 = 0 has roots that are equa

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

Options:

Correct Answer: 8

Solution:

For the roots to be equal, the discriminant must be zero. Thus, k^2 - 4*1*16 = 0, which gives k^2 = 64, so k = ±8.

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

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

Step 1: Understand that the equation is x^2 + kx + 16 = 0.
Step 2: Identify that for the roots of a quadratic equation to be equal, the discriminant must be zero.
Step 3: Recall the formula for the discriminant, which is given by D = b^2 - 4ac, where a, b, and c are the coefficients of the equation ax^2 + bx + c.
Step 4: In our equation, a = 1, b = k, and c = 16.
Step 5: Substitute the values into the discriminant formula: D = k^2 - 4*1*16.
Step 6: Simplify the equation: D = k^2 - 64.
Step 7: Set the discriminant equal to zero for equal roots: k^2 - 64 = 0.
Step 8: Solve for k by adding 64 to both sides: k^2 = 64.
Step 9: Take the square root of both sides: k = ±8.

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