What is the value of k for which the equation x^2 + kx + 16 = 0 has equal roots?

What is the value of k for which the equation x^2 + kx + 16 = 0 has equal roots?

Step 1: Understand that for a quadratic equation ax^2 + bx + c = 0 to have equal roots, the discriminant must be zero.
Step 2: Identify the coefficients from the equation x^2 + kx + 16 = 0. Here, a = 1, b = k, and c = 16.
Step 3: Write the formula for the discriminant: D = b^2 - 4ac.
Step 4: Substitute the values of a, b, and c into the discriminant formula: D = k^2 - 4*1*16.
Step 5: Simplify the equation: 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.
Step 9: The possible values for k are 8 and -8.

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