If |ax^2 + bx+c|<=1 for all x is [0, 1]...

If `|ax^2 + bx+c|<=1` for all x is `[0, 1]`,then

`|a|le8`

`|b|lgt8`

`|c|le1`

`|a|+|b|+|c|le17`

Text Solution

Verified by Experts

On putting `x=0,1` and `1/2` we get
`|c|le1`………..i
`|a+b+c|le1`…………ii
and `|a+2b+4c|le4`……….iii
From eqs i,ii and iii we get
`|b|le8` and `|a|le8`
`implies|a|+|v|+|c|le17`

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