x^3-8x^2>0 — step-by-step solution

Let's solve in

ℝ

x^{3} - 8 x^{2} > 0

You can write the expression:

x^{3} - 8 x^{2}

in factored form:

x^{2} \cdot (x - 8)

Let's solve in

ℝ

x^{2} > 0

Given the quadratic form

a x^{2} + b x + c

, let's compute the discriminant:

Δ = b^{2} - 4 a c

Δ = 0^{2} - 4 \cdot 1 \cdot 0

Δ = 0

Since

Δ = 0

, the equation has one solution:

For the unique solution, we obtain:

- \frac{b}{2 a}

Solution obtained:

x \in ℝ \ {0}

Let's solve in

ℝ

x - 8 > 0

Solution found:

x > 8

Let's build the table of the different terms to determine the global solution:

▶Solution found:

x \in (8, +∞)