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Question

The number of real values of x for which the equality |3x2+12x+6|=5x+16 holds good is


A

4

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B

3

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C

2

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D

1

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Solution

The correct option is C

2


Equation |3x2+12x+6|=5x+16 ......(i)

when 3x2+12x+60x2+4x2

|x+2|242|x+2|(2)2

⇔ x + 2 ≤ - 2 or x + 2 ≥ 2.......(ii)

Then (i) becomes 3x2+12x+6=5x+16

3x2+7x10=0 ⇒ x = 1, -103

But x = -103 does not satisfy (ii)

When 3x2+12x+6<0x2+4x>2

|x+2|222x2+2....(iii)

3x2+17x+22=0x=2,113

But x = - 113 does not satisfy (iii). So, 1 and -2 are the only solutions.


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