AP EAMCET · Maths · Quadratic Equation
The roots of the equation \(\left|x^2-x-6\right|=x+2\) are
- A \(-2,1,4\)
- B \(0,2,4\)
- C \(0,1,4\)
- D \(-2,2,4\)
Answer & Solution
Correct Answer
(D) \(-2,2,4\)
Step-by-step Solution
Detailed explanation
Given, \(\left|x^2-x-6\right|=x+2\) \(\begin{array}{ll} \Rightarrow & x^2-x-6=x+2 \\ \text {Or } & x^2-x-6=-x-2 \\ \Rightarrow & x^2-2 x-8=0 \text { or } x^2=4 \\ \Rightarrow & (x=-2,4) \text { or }(x= \pm 2) \Rightarrow x=\{-2,2,4\} \end{array}\)
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