NIMCET 2008 Question Paper with solutions

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Question : 19 of 120

Marks: +1, -0

The number of roots of the equation

|x^{2}-x-6|=x+2

is

2
3
4
None of these

Solution:

|x^{2}-x-6|=x+2

⇒ |(x-3)(x+2)|=x+2

⇒ (x-3)(x+2)=(x+2)

if

x ≤-2

or

x ≥ 3

and

-(x-3)(x+4)=(x+2)

if

-2 ≤ x ≤ 3

⇒ (x+2)(x-4)=0

if

x ≤-2

or

x ≥ 3

and

(x+2)(x-2)=0

if

-2 ≤ x ≤ 3

⇒ x=-2,4,2

∴

The number of roots is

3 .

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