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If c lt a lt b lt d, then roots of the e...

If `c lt a lt b lt d`, then roots of the equation `bx^(2)+(1-b(c+d)x+bcd-a=0`

A

are real and one lies between `c` and `a`

B

are real and distinct in which one lies between `a` and `b`

C

are real and distinct in which one lies between `c` and `d`

D

are not real

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `bx^(2)+(1-b(c+d)x+bcd-a=0`
`implies bx^(2)+x-bcx-bdx+bcd-a=0`
`impliesbx(x-c)-bd(x-c)+x-a=0`
`implies b(x-c)(x-d)+(x-a)=0`
Let `f(x)=b(x-c)(x-d)+(x-a)`
`:.f(c )=c-a lt 0` , `f(d)=d-a gt 0`
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