What is the value of k if the equation x² - 4x + k = 0 has no real roots? (2021)

What is the value of k if the equation x² - 4x + k = 0 has no real roots? (2021)

Step 1: Identify the equation given, which is x² - 4x + k = 0.
Step 2: Recognize that for a quadratic equation to have no real roots, the discriminant must be less than zero.
Step 3: The discriminant formula for the equation ax² + bx + c is given by D = b² - 4ac.
Step 4: In our equation, a = 1, b = -4, and c = k.
Step 5: Substitute the values into the discriminant formula: D = (-4)² - 4*1*k.
Step 6: Calculate (-4)², which is 16, so we have D = 16 - 4k.
Step 7: Set up the inequality for no real roots: 16 - 4k < 0.
Step 8: Solve the inequality: 16 < 4k.
Step 9: Divide both sides by 4: 4 < k.
Step 10: Rewrite the result: k > 4.

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