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

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

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

Step 1: Identify the quadratic equation, which is 2x^2 - 4x + k = 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 = 2, b = -4, and c = k.
Step 4: Substitute the values of a, b, and c into the discriminant formula: D = (-4)^2 - 4*2*k.
Step 5: Calculate (-4)^2, which is 16, so we have D = 16 - 8k.
Step 6: For the quadratic equation to have no real roots, the discriminant must be less than zero: 16 - 8k < 0.
Step 7: Rearrange the inequality: 16 < 8k.
Step 8: Divide both sides by 8: 2 < k.
Step 9: This means k must be greater than 2 for the equation to have no real roots.

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