EquationsMCQMTP June 22Question 1088 of 221
All Questions

Roots of the equation $2x^2 + 3x + 7 = 0are\displaystyle areα<span\displaystyle \alpha<span class="katex">and\displaystyle andβ\displaystyle \beta$ then the value of $α−1+β−1\displaystyle \alpha^{-1} + \beta^{-1}$ is

Select Your Answer (Keyboard: A, B, C, D)
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option d — −3/7\displaystyle -3/7

All Options:

  • A2\displaystyle 2
  • B3/7\displaystyle 3/7
  • C7/2\displaystyle 7/2
  • D−3/7\displaystyle -3/7

Detailed Solution & Explanation

Given the quadratic equation:
2x2+3x+7=02x^2 + 3x + 7 = 0
Let the roots be α\displaystyle α\displaystyle \alpha and β\displaystyle β\displaystyle \beta.
Using Vieta's formulas:
α+β=−ba=−32α+β\displaystyle \alpha + \beta = -ba\displaystyle \frac{b}{a} = -32\displaystyle \frac{3}{2}
αβ=ca=72α\displaystyle \alphaβ=ca=72\displaystyle \beta = \frac{c}{a} = \frac{7}{2}

We need to find the value of α−1+β−1\displaystyle α−1+β−1\displaystyle \alpha^{-1} + \beta^{-1}:
α−1+β−1=1α+1β=α+βαβ\displaystyle \alpha^{-1} + \beta^{-1} = \frac{1}{α\displaystyle \alpha} + \displaystyle \frac{1}{\beta} = \frac{\displaystyle \alpha + \beta}{α\displaystyle \alphaβ\displaystyle \beta}
Substitute the values of the sum and product:
1α+1β=−3/27/2=−37\displaystyle \frac{1}{\alpha} + \frac{1}{β\displaystyle \beta} = −3/27/2\displaystyle \frac{-3/2}{7/2} = -37\displaystyle \frac{3}{7}
This corresponds to Option d.

**Option d**

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 3x+y+2x−y\displaystyle \frac{3}{x+y} + \frac{2}{x-y} = -1 and 1x+y−1x−y=43\displaystyle 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 = 15−26\displaystyle \frac{1}{5-2\sqrt{6}}

The cost of 2\displaystyle 2 oranges and 3\displaystyle 3 apples is $28$. If the cost of an apple is doubled then the cost of $3orangesand\displaystyle oranges and5$ apples is $75$. The original cost of 7\displaystyle 7 oranges and 4\displaystyle 4 apples (in Rs) is:

In a multiple choice question paper consisting of $100questionsof\displaystyle questions of1\displaystyle mark each, a candidate gets &#36;60\% marks. If the candidate attempted all questions and there was a penalty of $0.25$ marks for wrong answers is:

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