The equation x^2 - 4x + k = 0 has no real roots if k is:
Practice Questions
1 question
Q1
The equation x^2 - 4x + k = 0 has no real roots if k is:
< 4
≥ 4
≤ 4
> 4
The discriminant must be less than zero: (-4)^2 - 4*1*k < 0 leads to k > 4.
Questions & Step-by-step Solutions
1 item
Q
Q: The equation x^2 - 4x + k = 0 has no real roots if k is:
Solution: The discriminant must be less than zero: (-4)^2 - 4*1*k < 0 leads to k > 4.
Steps: 9
Step 1: Identify the equation given: x^2 - 4x + k = 0.
Step 2: Recognize that this is a quadratic equation in the form of ax^2 + bx + c = 0, where a = 1, b = -4, and c = k.
Step 3: Understand that the discriminant (D) of a quadratic equation determines the nature of its roots. The formula for the discriminant is D = b^2 - 4ac.
Step 4: Substitute the values of a, b, and c into the discriminant formula: D = (-4)^2 - 4*1*k.
Step 5: Simplify the expression: D = 16 - 4k.
Step 6: For the equation to have no real roots, the discriminant must be less than zero: 16 - 4k < 0.
