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The number of real value of x for which the equality holds good is
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a
4
b
3
c
2
d
1
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Correct option is C
Equation is 3x2+12x+6=5x+16 ...(i)when 3x2+12x+6≥0⇔x2+4x≥-2⇔x+22≥4-2⇔x+2≥(2)2⇔x+2≤-2 or x+2≥2 ...(ii)Then (i) becomes 3x2+12x+6=5x+16⇔3x2+7x-10=0⇒x=1, -103But x=-103 does not satisfy (ii).when 3x2+12x+6<0⇒x2+4x<-2⇒x+2≤2⇒-2-2≤x≤-2+2 ...(iii)Then (i) becomes ⇒3x2+12x+6=-(5x+16)⇒3x2+17x+22=0⇒x=-2, -113But x=-113 does not satisfy (iii). So, 1 and -2 are the only solutions.
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