Question

X^2(x-1)(x-2)=<0а)-2;б)0;в)2;г)1;д)-1​

Answer 1

х²≤0

х≤0

х-1≤0

х≤1

х-2≤0

х≤2

Ответ: б), в), г)

Answer 2

Ответ:

незачто!!!!!!!!!!!!!!!

Answer 3

To solve the inequality $x^2(x-1)(x-2) \leq 0$, we can use a sign analysis approach. We need to find the intervals where the expression is less than or equal to zero.

First, let's find the critical points by setting each factor to zero:

1. $x^2 = 0$ has a double root at $x = 0$.
2. $x - 1 = 0$ gives $x = 1$.
3. $x - 2 = 0$ gives $x = 2$.

Now, we'll consider the sign of the expression $x^2(x-1)(x-2)$ in the intervals defined by these critical points: $(- \infty, 0)$, $(0, 1)$, $(1, 2)$, and $(2, \infty)$.

1. For $x < 0$:

   • $x^2$ is positive.
   • $x-1$ is negative.
   • $x-2$ is negative.

   The product $x^2(x-1)(x-2)$ is positive.

2. For $0 < x < 1$:

   • $x^2$ is positive.
   • $x-1$ is negative.
   • $x-2$ is negative.

   The product $x^2(x-1)(x-2)$ is negative.

3. For $1 < x < 2$:

   • $x^2$ is positive.
   • $x-1$ is positive.
   • $x-2$ is negative.

   The product $x^2(x-1)(x-2)$ is non-positive (zero or negative).

4. For $x > 2$:

   • $x^2$ is positive.
   • $x-1$ is positive.
   • $x-2$ is positive.

   The product $x^2(x-1)(x-2)$ is positive.

Now, based on this analysis, the solution to the inequality $x^2(x-1)(x-2) \leq 0$ is the interval $[0, 1] \cup [2, \infty)$.

So, the correct answer from the options provided is: в) 2