Question 373566
x^3-2x - 24 + 5x^2 ≤ 0
 
let study the roots of : x^3 + 5x^2 -2x - 24 = 0
 
Guess x=2 : 8 + 20 - 4 - 24 =0, 2 is a root, hence we can expand in terms like P(x)*(x-2)
 
x^3 - 2x^2 + 7x^2 - 14x + 12x - 24
 
=x^2(x-2) +7x(x-2) + 12(x-2)
 
=(x-2)(x^2 + 7x + 12)
 
=(x-2)(x+3)(x+4)
 
hence the two curves cross at 2, -3, -4
 
the inequality holds when the polynomial is negative, hence for
 
Solution if : x<-4 and x in [-3;2]


 
solution if green curve is greater than the red one :
 
{{{ graph( 300, 200, -5, 3, -100, 30, x^3-2x, 24 - 5x^2 ) }}}