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If the quadratic equation 4x^(2) -2(a+c-1)x + ac-b (a gt b gt c) then:

Answer»

Both roots are greater than a
Both roots are less than c
Both roots are lie in `(c/2, b/2)`
Exactly one root lie in `(c/2, a/2)`

Solution :`4x^(2)- 2ax - 2cx + 2X + ac -b=0`
`2x(2x-a) -c(2x -a) + 2x-b=0`
`f(x) = (2x-a)(2x-c) + (2x-b)=0`
`f(a/2) = a-bf(c/2)=c-b`
`f(a/2)f(c/2)=(a-b)(c-b) lt 0`
`therefore (a GT b gt c)`
So exactly one root lie in `(c/2, a/2)`


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