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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Complex Number

NDA 2021 · Mathematics · Complex Number

Consider the following statements in respect of the roots of the...

Consider the following statements in respect of the roots of the equation x3−8=0x^3-8=0 : 1. The roots are non-collinear. 2. The roots lie on a circle of unit radius. Which of the above statements is/are correct?

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

A. 1 only

Step-by-step solution

<br/><br/>x3−8=0⇒(x−2)(x2+2x+4)=0∴x=2,−1+3i,−1−3i\begin{aligned} & x^3-8=0 \\ & \Rightarrow(x-2)\left(x^2+2 x+4\right)=0 \\ & \therefore x=2,-1+\sqrt{3} i,-1-\sqrt{3} i \end{aligned}$$ So, roots non-collinear and lie on a circle of radius 2 units.
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