The quadratic equation 2x^2 - 4x + k = 0 has no real roots. What is the conditio

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Question: The quadratic equation 2x^2 - 4x + k = 0 has no real roots. What is the condition for k? (2022)

Options:

Correct Answer: k > 8

Exam Year: 2022

Solution:

The discriminant must be less than zero: (-4)^2 - 4*2*k < 0 leads to k > 8.

The quadratic equation 2x^2 - 4x + k = 0 has no real roots. What is the condition for k? (2022)

The quadratic equation 2x^2 - 4x + k = 0 has no real roots. What is the condition for k? (2022)

Step 1: Identify the quadratic equation, which is 2x^2 - 4x + k = 0.
Step 2: Recall that a quadratic equation has no real roots if its discriminant is less than zero.
Step 3: The discriminant (D) for the equation ax^2 + bx + c = 0 is given by the formula D = b^2 - 4ac.
Step 4: In our equation, a = 2, b = -4, and c = k.
Step 5: Substitute the values into the discriminant formula: D = (-4)^2 - 4*2*k.
Step 6: Calculate (-4)^2, which is 16, so we have D = 16 - 8k.
Step 7: Set the condition for no real roots: 16 - 8k < 0.
Step 8: Solve the inequality: 16 < 8k.
Step 9: Divide both sides by 8: 2 < k.
Step 10: Rewrite the result: k > 2.

No concepts available.