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if c!=0 and the equation p/(2x)=a/(x+c)+...

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

A

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

B

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

C

a+ b

D

a - b

Text Solution

Verified by Experts

The correct Answer is:
1.2
We can write the given equation as
` (p)/(2x) = ((a + b) x + c(b - a))/(x^(2) - c^(2))`
or ` p(x^(2) - c^(2)) = 2 (a + b) x^(2) - 2 c (a - b) x `
or `(2a + 2b - p )x^(2) - 2c (a - b) x + pc^(2) = 0`
for this equation to have equal roots,
`c^(2) (a - b)^(2) - pc^(2) (2a + 2b - p) = 0 `
or ` (a - b)^(2) - 2p (a + b) + p^(2) = 0 [ because c^(2) ne 0 ]`
or `[ p - (a + b)]^(2) = (a + b)^(2) - (a - b)^(2) = 4ab`
or ` p - (a + b) = pm 2 sqrt(ab)`
or `p = a + b pm 2 sqrt(ab) = (sqrt(a ) pm sqrt(b))^(2)` .
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  • If c ne 0 and the equation (p)/(2x)=(a)/(x+c)+(b)/(x-c) has two equal roots, then p can be

    A
    `(sqrt(a)-sqrt(b))^(2)`
    B
    `(sqrt(a)+sqrt(b))^(2)`
    C
    `a+b`
    D
    `a-b`

  • If a(b-c) x^(2)+b (c-a) x+c (a-b)=0 has equal roots, then 2/b=

    A
    `(1)/(a) +(1)/(c )`
    B
    `a+c`
    C
    `1//a+c`
    D
    `a+1//c`

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

    A
    equal roots
    B
    irrational roots
    C
    rational roots
    D
    none of these

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