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The number of roots of the equation ((x+...

The number of roots of the equation `((x+2)(x-5))/((x-3)(x+6))=(x-2)/(x+4)` is

A

`0`

B

`1`

C

`2`

D

`3`

Text Solution

Verified by Experts

The correct Answer is:
B
We have given `((x+2)(x-5))/((x-3)(x+6))=(x-2)/(x+4)`
`implies(x+2)(x−5)(x+4)−(x−2)(x−3)(x+6)`
`implies(x^3+x^2−22x−40)−(x^3+x^2−24x+36)=0`
`implies2x−76=0`
`impliesx=38`
Hence the number of roots are only 1.
Correct option is (b)
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Knowledge Check

  • The number of roots of the equation |x|=x^(2) +x -4 is :

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    4
    B
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    1
    D
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  • The number of roots of the equation x^(log_X(x+3)^2)=16 is

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  • The number of roots of the equation sqrt((x)/(x - 3)) + sqrt((x - 3)/( x)) = (5)/(2), x ne 0, x ne 3 is

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