EquationsMCQMTP May 19Question 1068 of 221
All Questions

When two roots of quadratic equations are α\displaystyle \alpha and 1α\displaystyle \frac{1}{\alpha} then what will be quadratic equation.

Options

Aax2−(α2+1)x+α=0\displaystyle ax^2 - (\alpha^2+1)x + \alpha = 0
Bax2−(α2+1)x+α=0\displaystyle ax^2 - (\alpha^2+1)x + \alpha = 0
Cax2−(a2+1)x+1=0\displaystyle ax^2 - (a^2+1)x + 1 = 0
DNone of these
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option c — ax2−(a2+1)x+1=0\displaystyle ax^2 - (a^2+1)x + 1 = 0

All Options:

  • Aax2−(α2+1)x+α=0\displaystyle ax^2 - (\alpha^2+1)x + \alpha = 0
  • Bax2−(α2+1)x+α=0\displaystyle ax^2 - (\alpha^2+1)x + \alpha = 0
  • Cax2−(a2+1)x+1=0\displaystyle ax^2 - (a^2+1)x + 1 = 0
  • DNone of these

Ad

Detailed Solution & Explanation

Given the roots of the quadratic equation:
x1=α\displaystyle x_1 = \alpha and x2=1α\displaystyle x_2 = \frac{1}{\alpha}

The standard form of a quadratic equation is:
x2−(x1+x2)x+x1x2=0x^2 - (x_1 + x_2)x + x_1x_2 = 0
Substitute the sum and product of the roots:
x1+x2=α+1α=α2+1αx_1 + x_2 = \alpha + \frac{1}{\alpha} = \frac{\alpha^2 + 1}{\alpha}
x1x2=α⋅1α=1x_1x_2 = \alpha \cdot \frac{1}{\alpha} = 1

Construct the equation:
x2−(α2+1α)x+1=0x^2 - \left(\frac{\alpha^2 + 1}{\alpha}\right)x + 1 = 0
Multiply the entire equation by α\displaystyle \alpha:
αx2−(α2+1)x+α=0\alpha x^2 - (\alpha^2 + 1)x + \alpha = 0

If we write the equation in terms of the parameter a\displaystyle a instead of α\displaystyle \alpha (which is a common notation choice in CA exam options):
ax2−(a2+1)x+a=0ax^2 - (a^2 + 1)x + a = 0
This matches Option c (with a minor typo in the constant term being +1\displaystyle +1 instead of +a\displaystyle +a).
**Option c**

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

If 3x+y+2x−y=−1\displaystyle \frac{3}{x+y} + \frac{2}{x-y} = -1 and 1x+y−1x−y=43\displaystyle \frac{1}{x+y} - \frac{1}{x-y} = \frac{4}{3} then (x,y)\displaystyle (x, y) is:

2x+510+3x+1015=5\displaystyle \frac{2x+5}{10} + \frac{3x+10}{15} = 5, find x\displaystyle x

Find value of x2−10x+1\displaystyle x^2 - 10x + 1 if x=15−26\displaystyle x = \frac{1}{5-2\sqrt{6}}

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

Ready to Master Equations?

Practice all 221 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free