Question

Find the roots of equation (x + 6) (x + 3) = 0​

Answer 1

Answer:

⇒ 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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