EquationsPYQ Sept 25Question 4405 of 155
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The roots of the equation (xx−1)2−5(xx−1)+6=0\displaystyle \left(\frac{x}{x-1}\right)^2 - 5\left(\frac{x}{x-1}\right) + 6 = 0 are:

Options

A2, 3/2
B3, 1/2
C2, 1/3
D3, 2/3
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Correct Answer

✅ Option a — 2, 3/2

All Options:

  • A2, 3/2
  • B3, 1/2
  • C2, 1/3
  • D3, 2/3

Detailed Solution & Explanation

Given equation: (xx−1)2−5(xx−1)+6=0\left(\frac{x}{x-1}\right)^2 - 5\left(\frac{x}{x-1}\right) + 6 = 0
Let us substitute y=xx−1\displaystyle y = \frac{x}{x-1}. The equation simplifies to: y2−5y+6=0y^2 - 5y + 6 = 0
Factoring this quadratic equation: (y−2)(y−3)=0(y - 2)(y - 3) = 0 This gives two cases:
**Case 1:** y=2\displaystyle y = 2 xx−1=2  ⟹  x=2(x−1)\frac{x}{x-1} = 2 \implies x = 2(x-1) x=2x−2  ⟹  x=2x = 2x - 2 \implies x = 2
**Case 2:** y=3\displaystyle y = 3 xx−1=3  ⟹  x=3(x−1)\frac{x}{x-1} = 3 \implies x = 3(x-1) x=3x−3  ⟹  2x=3  ⟹  x=32x = 3x - 3 \implies 2x = 3 \implies x = \frac{3}{2}
Thus, the roots of the equation are 2\displaystyle 2 and 3/2\displaystyle 3/2.
Hence, **Option A** is the correct answer.

About This Chapter: Equations

Paper

Paper 3: Quantitative Aptitude

Weightage

4-6 Marks

Key Topics

Linear, Quadratic and Cubic Equations

This chapter covers Linear, Quadratic and Cubic Equations and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 4-6 Marks weightage. Focus on understanding core concepts rather than memorizing.

More Questions from Equations

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The cost of 2\displaystyle 2 oranges and 3\displaystyle 3 apples is 28\displaystyle 28. If the cost of an apple is doubled then the cost of 3\displaystyle 3 oranges and 5\displaystyle 5 apples is 75\displaystyle 75. The original cost of 7\displaystyle 7 oranges and 4\displaystyle 4 apples (in Rs) is:

In a multiple choice question paper consisting of 100\displaystyle 100 questions of 1\displaystyle 1 mark each, a candidate gets 60%\displaystyle 60\% marks. If the candidate attempted all questions and there was a penalty of 0.25\displaystyle 0.25 marks for wrong answers is:

The values of x\displaystyle x and y\displaystyle y satisfying the equations 3x+y+2x−y=3\displaystyle \frac{3}{x+y} + \frac{2}{x-y} = 3 and 2x+y+3x−y=233\displaystyle \frac{2}{x+y} + \frac{3}{x-y} = \frac{23}{3} given by

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