Question

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

• A. $(2,0)$
• B. $(-2,0)\cup (\frac{3}{2},\infty )$
• C. $(0,3)$
• D. None of these

Answer 1

The correct option is B $(-2,0)\cup (\frac{3}{2},\infty )$

R.E.F image

Given inequality

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

$2x^3+x^2-6x>0$

$x(2x^2+x-6)>0$

$x(2x^2+4x-3x-6)>0$

$x\left(2x\right(x+2)-3(x+2\left)\right)>0$

$x(2x-3)(x+2)>0\to \left(1\right)$

using numbers lines

Given inequality (1) is greater than 0

So, $xϵ(-2,0)\cup (\frac{3}{2},\infty )$

Hence correct option is B.