Question

X^3-3x^2-8x+24=0 Помогите плиз. Легко, но неумею(

Answer 1

Х^3-3х^2-8х+24=0
х^2*(х-3)-8(х-3)=0
(х^2-8)(х-3)=0
х^2-8=0
х-3=0
Х1=2корня из2
Х2=-2корня из2
Х3=3

Answer 2

Solving the Equation X^3 - 3x^2 - 8x + 24 = 0

To solve the equation X^3 - 3x^2 - 8x + 24 = 0, we can use various methods such as factoring, the rational root theorem, or numerical methods. Let's explore the solution using the rational root theorem.

The rational root theorem states that if a rational number p/q (in lowest terms) is a root of a polynomial equation with integer coefficients, then p is a factor of the constant term and q is a factor of the leading coefficient.

First, let's list all the possible rational roots of the equation. The possible rational roots are all the factors of the constant term (24) divided by all the factors of the leading coefficient (1).

The factors of 24 are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24. The factors of 1 are ±1.

Therefore, the possible rational roots are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24.

We can then use these possible rational roots to test for solutions using synthetic division or other methods.

Let's proceed with finding the roots of the equation using the rational root theorem and the possible rational roots.

X^3 - 3x^2 - 8x + 24 = 0

I hope this helps! Let me know if you need further assistance.