The equation x-2-x-1-1-2-x-1 hasA- Infinitely many rootsB- One RootC- No rootD- Two Roots

The correct option is C No root x 2/x 1 =1 2/x 1————— (1) ⟹x^2 x 2 = x 1 2 ⟹x^2 x+1 =0 ⟹(x 1)^2 0 ⟹ x 1 = 0⟹ x=1 But when x=1 (1) is not divided ∴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 roots

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Solution

The correct option is A
No root

x- $\frac{2}{x - 1}$ =1 - $\frac{2}{x - 1}$ ----------------(1)

$⟹$ $x^{2} - x - 2$ = x-1-2

$⟹$ $x^{2} - x + 1$ =0

$⟹$ $(x - 1)^{2}$ -0

$⟹$ x-1 = 0 $⟹$ x=1

But when x=1 (1) is not divided $∴$ No root

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The equation x-2x−1=1 -2x−1 has

The correct option is A No root x-2x−1 =1 -2x−1----------------(1) ⟹x2−x−2 = x-1-2 ⟹x2−x+1 =0 ⟹(x−1)2-0 ⟹ x-1 = 0⟹ x=1 But when x=1 (1) is not divided ∴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)

$⟹$ $x^{2} - x - 2$ = x-1-2

$⟹$ $x^{2} - x + 1$ =0

$⟹$ $(x - 1)^{2}$ -0

$⟹$ x-1 = 0 $⟹$ x=1

But when x=1 (1) is not divided $∴$ No root