EquationsMCQMTP Sep 24 Series IQuestion 1102 of 221
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If α\displaystyle α\displaystyle \alpha and β\displaystyle β\displaystyle \beta are roots of the equation x2−8x+12=0\displaystyle x^2 - 8x + 12 = 0 then 1/α+1/β=\displaystyle 1/α+1/β\displaystyle \alpha + 1/\beta =

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option a — 2/3\displaystyle 2/3

All Options:

  • A2/3\displaystyle 2/3
  • B2/4\displaystyle 2/4
  • C3/4\displaystyle 3/4
  • D4/5\displaystyle 4/5

Detailed Solution & Explanation

For the quadratic equation x2−8x+12=0\displaystyle x^2 - 8x + 12 = 0, let the roots be α\displaystyle α\displaystyle \alpha and β\displaystyle β\displaystyle \beta.

Using Vieta's formulas:
1. Sum of roots: α+β=−−81=8\displaystyle α+β\displaystyle \alpha + \beta = -−81=8\displaystyle \frac{-8}{1} = 8
2. Product of roots: αβ=121=12\displaystyle α\displaystyle \alpha β=121=12\displaystyle \beta = \frac{12}{1} = 12

We need to find the value of 1α+1β\displaystyle \displaystyle \frac{1}{\alpha} + \frac{1}{β\displaystyle \beta}:
1α+1β=α+βαβ\displaystyle \frac{1}{\alpha} + \frac{1}{β\displaystyle \beta} = α+βαβ\displaystyle \frac{\alpha + \beta}{\alpha \beta}
Substituting the sum and product values:
1α+1β=812=23\displaystyle \frac{1}{\alpha} + \frac{1}{β\displaystyle \beta} = 812=23\displaystyle \frac{8}{12} = \frac{2}{3}

Hence, the correct option is **Option (a)**.

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.

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