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IF [x^(2) - 2x + a]=0 has no solution, t...

IF `[x^(2) - 2x + a]=0` has no solution, then find the values of a (where `[*] ` represents the greatest integer).

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We have `[x^(2) - 2x + a]=0`
`rArr x^(2) - 2x + a in` [ 0, 1)
So, equation has no solution if `x^(2) - 2x a notin` [0, 1).
`therefore x^(2) - 2x + a lt AA x in` R, which is not possible.
So, `x^(2) - 2x + a lt 1 AA x in` R
`rArr x^(2) - 2x + a - 1 ge 0, AA x in` R
Now, `Dge 0`
`rArr 4-4 (a- 1) le 0`
`rArr 2 - a le 0`
`rArr a ge 2`
`rArr a in [ 2, infty)`
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