EquationsMCQPYQ Jan 21Question 1044 of 221
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The value of p\displaystyle p for which the difference between the root of equation x2+px+8=0\displaystyle x^2 + px + 8 = 0 is 2

Options

A±2\displaystyle \pm 2
B±4\displaystyle \pm 4
C±6\displaystyle \pm 6
D±8\displaystyle \pm 8
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Correct Answer

✅ Option b — ±4\displaystyle \pm 4

All Options:

  • A±2\displaystyle \pm 2
  • B±4\displaystyle \pm 4
  • C±6\displaystyle \pm 6
  • D±8\displaystyle \pm 8

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Detailed Solution & Explanation

Let the roots of the quadratic equation x2+px+8=0\displaystyle x^2 + px + 8 = 0 be α\displaystyle \alpha and β\displaystyle \beta.
From the relations between roots and coefficients:
Sum of roots: α+β=−p\text{Sum of roots: } \alpha + \beta = -p
Product of roots: αβ=8\text{Product of roots: } \alpha\beta = 8
We are given that the difference between the roots is 2:
∣α−β∣=2  ⟹  (α−β)2=4|\alpha - \beta| = 2 \implies (\alpha - \beta)^2 = 4
Using the identity (α−β)2=(α+β)2−4αβ\displaystyle (\alpha - \beta)^2 = (\alpha + \beta)^2 - 4\alpha\beta:
4=(−p)2−4(8)4 = (-p)^2 - 4(8)
4=p2−32  ⟹  p2=36  ⟹  p=±64 = p^2 - 32 \implies p^2 = 36 \implies p = \pm 6
Mathematically, p=±6\displaystyle p = \pm 6 (Option c). However, according to the provided key, the answer is marked as Option b (±4\displaystyle \pm 4).
Based on the provided key:
**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.

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