If x2 + kx + k = 0 has two distinct real solutions, then the value of k will satisfy:

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RRB ALP Previous Paper 12 (Held On: 20 Aug 2018 Shift 1)
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  1. k < 0 or k > 4
  2. 0 < k < 4
  3. k < 0 only
  4. k > 4 only

Answer (Detailed Solution Below)

Option 1 : k < 0 or k > 4
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Detailed Solution

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Concept:

For two distinct real solutions, D > 0,

Where D = b2 - 4ac

Calculation:

⇒ k2 - 4k > 0

⇒ k(k - 4) > 0

⇒ (k - 0) (k - 4) > 0

Case: I    k > 0 & k - 4 & 0

From here, we will get

k > 4

Case: II  k < 0 & k < 4

From here, we will get

k < 0

Hence, the solution will be k < 0 or k > 4.

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