If x'+x-6-0, then x-
1)2,-3
2)1,3
3)3,-2
4)-3, 2
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⇒ The given equation is ∣x∣
2
+∣x∣−6=0 ---- ( 1 )
⇒ When x≥0, then ∣x∣=x, so equation ( 1 ) becomes,
x
2
+x−6=0
⇒ x
2
+3x−2x−6=0
⇒ x(x+3)−2(x+3)=0
⇒ (x+3)(x−2)=0
⇒ x=−3,2
When x<0, then ∣x∣=−x, so equation ( 1 ) becomes,
x
2
−x−6=0
⇒ x
2
−3x+2x−6=0
⇒ x(x−3)+2(x−3)=0
⇒ (x−3)(x+2)=0
⇒ x=3,−2
⇒ Sum of the roots =−3+2+3−2=0
∴ Here, roots are real and equal.
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