For the quadratic equation 2x^2 + 4x + k = 0 to have equal roots, what should be

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Question: For the quadratic equation 2x^2 + 4x + k = 0 to have equal roots, what should be the value of k? (2020)

Options:

Correct Answer: -4

Exam Year: 2020

Solution:

For equal roots, the discriminant must be zero: b^2 - 4ac = 0. Here, 4^2 - 4(2)(k) = 0 leads to k = 4.

For the quadratic equation 2x^2 + 4x + k = 0 to have equal roots, what should be the value of k? (2020)

For the quadratic equation 2x^2 + 4x + k = 0 to have equal roots, what should be the value of k? (2020)

Step 1: Identify the quadratic equation, which is 2x^2 + 4x + k = 0.
Step 2: Recall that for a quadratic equation to have equal roots, the discriminant must be zero.
Step 3: The discriminant formula is b^2 - 4ac, where a, b, and c are the coefficients from the equation ax^2 + bx + c.
Step 4: In our equation, a = 2, b = 4, and c = k.
Step 5: Substitute the values into the discriminant formula: 4^2 - 4(2)(k) = 0.
Step 6: Calculate 4^2, which is 16, so we have 16 - 4(2)(k) = 0.
Step 7: Simplify the equation: 16 - 8k = 0.
Step 8: Rearrange the equation to solve for k: 8k = 16.
Step 9: Divide both sides by 8 to find k: k = 16 / 8.
Step 10: Calculate the final value: k = 2.

Discriminant of a Quadratic Equation – The discriminant (b^2 - 4ac) determines the nature of the roots of a quadratic equation. For equal roots, the discriminant must be zero.