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

Options

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

Answer

C

Explanation

`(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`