What is the value of k if the equation x^2 + kx + 4 = 0 has equal roots? (2022)

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Question: What is the value of k if the equation x^2 + kx + 4 = 0 has equal roots? (2022)

Options:

Correct Answer: 4

Exam Year: 2022

Solution:

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

What is the value of k if the equation x^2 + kx + 4 = 0 has equal roots? (2022)

What is the value of k if the equation x^2 + kx + 4 = 0 has equal roots? (2022)

Step 1: Understand that for a quadratic equation to have equal roots, the discriminant must be zero.
Step 2: Identify the standard form of a quadratic equation, which is ax^2 + bx + c = 0. In this case, a = 1, b = k, and c = 4.
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*4.
Step 5: Simplify the equation: D = k^2 - 16.
Step 6: Set the discriminant equal to zero for equal roots: k^2 - 16 = 0.
Step 7: Solve the equation k^2 - 16 = 0 by adding 16 to both sides: k^2 = 16.
Step 8: Take the square root of both sides to find k: k = ±4.

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