EquationsMCQPYQ Nov 20Question 1056 of 221
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The rational root of the equation 0=2p3−p2−4p+2\displaystyle 0 = 2p^3 - p^2 - 4p + 2 is:

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

✅ Option c — 12\displaystyle \frac{1}{2}

All Options:

  • A2
  • B-2
  • C12\displaystyle \frac{1}{2}
  • D14\displaystyle \frac{1}{4}

Detailed Solution & Explanation

Given the cubic equation:
2p3−p2−4p+2=02p^3 - p^2 - 4p + 2 = 0
We can solve this by grouping the terms:
(2p3−p2)−(4p−2)=0(2p^3 - p^2) - (4p - 2) = 0
Factor out the common terms:
p2(2p−1)−2(2p−1)=0p^2(2p - 1) - 2(2p - 1) = 0
(p2−2)(2p−1)=0(p^2 - 2)(2p - 1) = 0
Set each factor to zero to find the roots:
1) p2−2=0  ⟹  p2=2  ⟹  p=±2\displaystyle p^2 - 2 = 0 \implies p^2 = 2 \implies p = ±\displaystyle \pm2\displaystyle \sqrt{2} (these are irrational roots)
2) $2p - 1 = 0 \implies 2p = 1 \implies p = 12<span\displaystyle \frac{1}{2}<span class="katex">(thisisarationalroot)<br><br>Therefore,therationalrootis\displaystyle (this is a rational root)<br><br>Therefore, the rational root isp = 12\displaystyle \frac{1}{2}$, which is Option c.
**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.

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