The Equation x -2- x -1-1-2- x -1 hasA- no rootB- infinitely manyC- two rootsD- one root

The correct option is A no rootx 2/x 1=1 2/x 1—–(1) ⇒ x^2 x 2=x 1 2 ⇒ x^2 2x+1 =0 ⇒ (x 1)^2=0 ⇒ x 1 =0 ⇒ x =1 But when x = 1 (1) is not defined ∴ no root ...

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Standard XII

Mathematics

Relations between Roots and Coefficients : Higher Order Equations

The Equation ...

Question

The Equation $x - \frac{2}{x - 1} = 1 - \frac{2}{x - 1}$ has

no root

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one root

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two roots

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infinitely many

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Solution

The correct option is A no root
$x - \frac{2}{x - 1} = 1 - \frac{2}{x - 1} - - - - - (1) \Rightarrow x^{2} - x - 2 = x - 1 - 2 \Rightarrow x^{2} - 2 x + 1 = 0 \Rightarrow (x - 1)^{2} = 0 \Rightarrow x - 1 = 0 \Rightarrow x = 1$
But when x = 1 (1) is not defined $∴$ no root

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The Equation x−2x−1=1−2x−1 has

The correct option is A no rootx−2x−1=1−2x−1−−−−−(1)⇒x2−x−2=x−1−2⇒x2−2x+1=0⇒(x−1)2=0⇒x−1=0⇒x=1 But when x = 1 (1) is not defined ∴ no root

The Equation $x - \frac{2}{x - 1} = 1 - \frac{2}{x - 1}$ has

The correct option is A no root
$x - \frac{2}{x - 1} = 1 - \frac{2}{x - 1} - - - - - (1) \Rightarrow x^{2} - x - 2 = x - 1 - 2 \Rightarrow x^{2} - 2 x + 1 = 0 \Rightarrow (x - 1)^{2} = 0 \Rightarrow x - 1 = 0 \Rightarrow x = 1$
But when x = 1 (1) is not defined $∴$ no root