If c ne 0 and the equation (p)/(2x)=(a)/...

If `c ne 0` and the equation `(p)/(2x)=(a)/(x+c)+(b)/(x-c)` has two equal roots, then `p` can be

`(sqrt(a)-sqrt(b))^(2)`

`(sqrt(a)+sqrt(b))^(2)`

`a+b`

`a-b`

Text Solution

Verified by Experts

The correct Answer is:

A, B

`(a,b)` We have `(p)/(2x)=((a+b)x+c(b-a))/(x^(2)-c^(2))`
`implies p(x^(2)-c^(2))=2(a+b)x^(2)-2c(a-b)x`
`implies (2a+2b-p)x^(2)-2c(a-b)x+pc^(2)=0`
Since roots are equal
`D=c^(2)(a-b)^(2)-pc^(2)(2a+2b-p)=0`
`implies (a-b)^(2)-2p(a+b)+p^(2)=0 (:' c^(2) ne 0)`
`implies [p-(a+b)]^(2)=(a+b)^(2)-(a-b)^(2)`
`impliesp=a+b+-2sqrt(ab)=(sqrt(a)+-sqrt(b))^(2)`

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`(1)/(a) +(1)/(c )`

`a+c`

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`a+1//c`

The equation (b-c) x^(2)+ (c-a) x+(a-b)=0 has

equal roots

irrational roots

rational roots

none of these

If the roots of the equation (x-b) (x-c) + (x-c) (x-a) + (x-a) (x-b)=0 are equal, then

a+b+c =0

`a+b omega +c omega^(2)=0`

`a-b+c=0`

`a+b omega^(2)+c omega =0`