For which value of k does the equation x^2 + kx + 16 = 0 have equal roots? (2019

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Question: For which value of k does the equation x^2 + kx + 16 = 0 have equal roots? (2019)

Options:

Correct Answer: -4

Exam Year: 2019

Solution:

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

For which value of k does the equation x^2 + kx + 16 = 0 have equal roots? (2019)

For which value of k does the equation x^2 + kx + 16 = 0 have equal roots? (2019)

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, which is 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 expression: D = k^2 - 64.
Step 6: Set the discriminant equal to zero for equal roots: 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: Since the question asks for the value of k, we can choose k = -8.

Discriminant – The discriminant of a quadratic equation determines the nature of its roots; for equal roots, it must be zero.
Quadratic Equation – A polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are constants.