CBSE Class 10 Mathematics Basic 2026: question 32(b)

Hints

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Step-by-step solution

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1. $\frac{1}{x}-\frac{1}{x-2}=\frac{x-2-x}{x(x-2)}=3\Rightarrow \frac{-2}{x^2-2x}=3$.

   1 mark

2. $3x^2-6x=-2\Rightarrow 3x^2-6x+2=0$ (standard form).

   1 mark

3. Here $a=3,b=-6,c=2$; Discriminant $D=b^2-4ac=36-24=12$.

   1 mark

4. $x=\frac{-b\pm \sqrt{D}}{2a}=\frac{6+\sqrt{12}}{6}$ or $\frac{6-\sqrt{12}}{6}$.

   1 mark

5. Since $\sqrt{12}=2\sqrt{3}$, roots are $1+\frac{\sqrt{3}}{3}$ and $1-\frac{\sqrt{3}}{3}$.

   1 mark

Answer: $3x^2-6x+2=0$; roots $1+\frac{\sqrt{3}}{3}$ and $1-\frac{\sqrt{3}}{3}$

Revise the chapter

• Chapter: Quadratic Equations (notes, formulas, where marks are lost and every past question)
• Topic: Quadratic Formula