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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2019 · Mathematics · Quadratic Equation

What are the roots of the equation |x^2-x-6|=x+2 ?

What are the roots of the equation \left|x^2-x-6\right|=x+2 ?

Options

  1. A−2,1,4-2,1,4
  2. B0,2,40,2,4
  3. C0,1,40,1,4
  4. D−2,2,4-2,2,4

Correct answer

D. −2,2,4-2,2,4

Step-by-step solution

 Given, ∣x2−x−6∣=x+2∴x2−x−6=x+2 and  x2−x−6=−(x+2)⇒x2−2x−8=0⇒x2−x−6=−x−2⇒x2−4x+2x−8=0⇒x2=4⇒x(x−4)+2(x−4)=0⇒x=+2,−2⇒x=4,−2∴x=−2,2,4\begin{aligned} & \text{ Given, }\left|x^2-x-6\right|=x+2 \\ & \therefore x^2-x-6=x+2 \text{\text{ and } } x^2-x-6=-(x+2) \\ & \Rightarrow x^2-2 x-8=0 \\ & \Rightarrow x^2-x-6=-x-2 \\ & \Rightarrow x^2-4 x+2 x-8=0 \\ & \Rightarrow x^2=4 \\ & \Rightarrow x(x-4)+2(x-4)=0 \\ & \Rightarrow x=+2,-2 \\ & \Rightarrow x=4,-2 \\ & \therefore x=-2,2,4\end{aligned}
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