Given:
x² + kx + k = 0
The equation has no real solution.
Step 1: Use the discriminant condition.
For a quadratic equation ax² + bx + c = 0,
Discriminant, D = b² − 4ac
For no real roots,
D < 0
Step 2: Calculate the discriminant.
a = 1, b = k, c = k
D = k² − 4k
= k(k − 4)
Step 3: Apply the condition D < 0.
k(k − 4) < 0
This is true when k lies between the roots 0 and 4.
0 < k < 4
Answer:
0 < k < 4
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