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If c>0 and 4a+c<2b then ax^2-bx+c=0 has ...

If `c>0` and `4a+c<2b` then `ax^2-bx+c=0` has a root win which one of the following intervals a)(0,2) b)(2,3) c)(3,4) d)(-2,0)

Text Solution

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`f(x) = ax^2 - bx +c`
`f(0) = 0-0 +c`
`f(0) = c> 0`
`f(-2)=4a-2b+c`
`4a +c < 2b`
`4a +c - 2b < 0`
`f(2) < 0`
`f(0) > 0 & f(2) < 0`
...
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