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

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

Solution: For equal roots, the discriminant must be zero: k^2 - 4*1*16 = 0, thus k^2 = 64, giving k = -8 or k = 8. The answer is -8.

Steps: 9

Step 1: Identify the quadratic equation given, which is x^2 + kx + 16 = 0.
Step 2: Recall that for a quadratic equation ax^2 + bx + c = 0, the discriminant is given by the formula D = b^2 - 4ac.
Step 3: In our equation, 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: For the roots to be equal, set the discriminant D to 0: k^2 - 64 = 0.
Step 7: Solve the equation k^2 - 64 = 0 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. Since the question asks for the value of k, we can choose -8.