Let S denote The Set Of All Values Of The Parameter a for Which                          Has No Solution, Then S Equals

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Question

Let S denote the set of all values of the parameter a for which

                        

has no solution, then S equals

Solution

Correct option is

(– ∞, –1)

If a = 0, (1) holds for all x ≤ 0. Write (1) as

                    x2 + a = a2 – 2ax + x2

⇒               2ax = a(a – 1) ⇒ x = (a – 1)/2

Substituting this (1) we get   

This holds if a ≥ – 1.

∴ The equation has no solution if a < – 1.

Testing

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