The number of real roots of the equation x2-3xx2-1-2-1x-1-0 is

X^2 3xx^2 1+2+1x 1=0 ⇒ nbsp;x(x 3)(x+1)(x 1)+2(x 1)(x 1)+1x 1=0 ⇒1x^2 1[x(x 3)+2(x^2 1)+(x+1)]=0 here x^2 1≠0 ⇒ x≠±1 ⇒ x^2 3x+2x^2 2+x+1=0 ⇒ 3x^2 2x 1=0 ⇒ 3x ...

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Standard XI

Mathematics

Roots of a Quadratic Equation

The number of...

Question

The number of real roots of the equation $\frac{x^{2} - 3 x}{x^{2} - 1} + 2 + \frac{1}{x - 1} = 0$ is

1

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2

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infinitely many

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Solution

The correct option is A $1$
$\frac{x^{2} - 3 x}{x^{2} - 1} + 2 + \frac{1}{x - 1} = 0 \Rightarrow \frac{x (x - 3)}{(x + 1) (x - 1)} + \frac{2 (x - 1)}{(x - 1)} + \frac{1}{x - 1} = 0 \Rightarrow \frac{1}{x^{2} - 1} [x (x - 3) + 2 (x^{2} - 1) + (x + 1)] = 0 here x^{2} - 1 \neq 0 \Rightarrow x \neq \pm 1 \Rightarrow x^{2} - 3 x + 2 x^{2} - 2 + x + 1 = 0 \Rightarrow 3 x^{2} - 2 x - 1 = 0 \Rightarrow 3 x^{2} - 3 x + x - 1 = 0 \Rightarrow (x - 1) (3 x + 1) = 0 \Rightarrow x = - \frac{1}{3}$

Hence, the number of real roots is $1$ .

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Roots of a Quadratic Equation

Standard XI Mathematics

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The number of real roots of the equation x2−3xx2−1+2+1x−1=0 is

The correct option is A 1x2−3xx2−1+2+1x−1=0⇒x(x−3)(x+1)(x−1)+2(x−1)(x−1)+1x−1=0⇒1x2−1[x(x−3)+2(x2−1)+(x+1)]=0here x2−1≠0⇒x≠±1⇒x2−3x+2x2−2+x+1=0⇒3x2−2x−1=0⇒3x2−3x+x−1=0⇒(x−1)(3x+1)=0⇒x=−13 Hence, the number of real roots is 1.

The number of real roots of the equation $\frac{x^{2} - 3 x}{x^{2} - 1} + 2 + \frac{1}{x - 1} = 0$ is