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Question

$$2{ x }^{ 3 }+{ x }^{ 2 }>6x$$


A
(2,0)
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B
(2,0)(32,)
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C
(0,3)
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D
None of these
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Solution

The correct option is B $$(-2,0)\cup(\dfrac 32,\infty)$$
R.E.F image 
Given inequality 
$$ 2x^{3}+x^{2}>6x $$
$$ 2x^{3}+x^{2}-6x>0 $$ 
$$ x(2x^{2}+x-6)>0 $$
$$ x(2x^{2}+4x-3x-6)>0 $$
$$ x(2x(x+2)-3(x+2))>0 $$
$$ x(2x-3)(x+2)>0\rightarrow (1) $$
using numbers lines 
Given inequality (1) is greater than 0
So, $$ x\epsilon (-2,0)\cup (\dfrac{3}{2},\infty ) $$
Hence correct option is B. 

1140118_426603_ans_b6829fbd4ca1439f94d2ceacd0d7d804.png

Mathematics

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