[tex] {x}^{4} - 5 {x}^{3} - 24 {x}^{2} > 0 [/tex]
[tex] {x}^{2} ( {x}^{2} - 5x - 24) > 0[/tex]
[tex] {x}^{2} ( {x}^{2} - 5x - 24) = 0[/tex]
1)
[tex] {x}^{2} = 0[/tex]
[tex]x = 0[/tex]
2)
[tex] {x}^{2} - 5x - 24 = 0[/tex]
liczymy deltę (trójkąt)
[tex]delta = 25 - 4 \times 1 \times ( - 24) = 25 + 96 = 121[/tex]
[tex] \sqrt{delta} = \sqrt{121} = 11[/tex]
[tex] x_{1} = \frac{5 - 11}{2} = \frac{ - 6}{2} = - 3[/tex]
[tex] x_{2} = \frac{5 + 11}{2} = \frac{16}{2} = 8[/tex]
czyli
[tex] {x}^{2} (x + 3)(x - 8) > 0[/tex]
reszta zadania w załączniku :)
