Question

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

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

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 0So, $$x\epsilon (-2,0)\cup (\dfrac{3}{2},\infty )$$Hence correct option is B. Mathematics

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