How to check for range condition when a equation containing

misangela4gi

misangela4gi

Answered question

2022-04-21

How to check for range condition when a equation containing other function is converted into quadratic?
The least positive value of a for which 4xa×2xa+30 is satisfied by at least one real value of x is ?

Answer & Explanation

Leia Wiggins

Leia Wiggins

Beginner2022-04-22Added 18 answers

The interval where the discriminant is nonnegative is a(,6][2,).
For a=2, we have t22t+1=(t1)2 as the quadratic equation, and it is equal to zero when t=2x=1, which is certainly satisfied by some real value of x.
For 0<a<2, by your discriminant and leading coefficient argument, t2ata+3>0 for all t.
Hence the least positive value of a must be 2.

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