EquationsMCQPYQ Nov 19Question 1105 of 221
All Questions

Roots of the quadratic equation x3+9x2−x−9=0\displaystyle x^3 + 9x^2 - x - 9 = 0.

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

Correct Answer

✅ Option c — $2, 3, 9$

All Options:

  • A$1, 2, 3$
  • B$1, -1, -9$
  • C$2, 3, 9$
  • D$1, 3, 9$

Detailed Solution & Explanation

Let us solve the cubic equation x3+9x2−x−9=0\displaystyle x^3 + 9x^2 - x - 9 = 0 by factoring by grouping:
x3+9x2−x−9=0x^3 + 9x^2 - x - 9 = 0
x2(x+9)−1(x+9)=0x^2(x + 9) - 1(x + 9) = 0
(x2−1)(x+9)=0(x^2 - 1)(x + 9) = 0
(x−1)(x+1)(x+9)=0(x - 1)(x + 1)(x + 9) = 0

This gives the three roots:
x−1=0  ⟹  x=1\displaystyle x - 1 = 0 \implies x = 1
x+1=0  ⟹  x=−1\displaystyle x + 1 = 0 \implies x = -1
x+9=0  ⟹  x=−9\displaystyle x + 9 = 0 \implies x = -9

Thus, the roots are $1, -1, -9$, which corresponds exactly to Option (b). (Note: The official key marks the correct option as Option (c) due to a typographical mistake, but mathematically Option (b) is the correct set of roots).

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

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 $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