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Find the values of a for whilch the equa...

Find the values of `a` for whilch the equation `sin^4x+asin^2x+1=0` will have ea solution.

Text Solution

Verified by Experts

Let ` t = sin ^(2) x rArr t in [ 0 , 1] `
Hence , `t^(2) + at + 1 =0 ` should have at least one solution in [0,1]. Since
product of roots is positive and equal to one , equation must have
exactly one root in [0,1] . Hence ,
` f(1) lt 0 `
`rArr 2 + a lt 0 `
`rArr a in (-infty, - 2)` .
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