Question

2x^4-3x^3-x^2-3x+2=0

Answer 1

Решение смотри на фото

Answer 2

To solve this equation, we can use the method of factoring.

First, we can try to factor out any common factors. In this case, there are no common factors, so we move on to the next step.

Next, we can try to factor the equation by grouping terms together. We can group the first two terms and the last two terms as follows:

2x^4 - 3x^3 - x^2 - 3x + 2 = (2x^4 - 3x^3) - (x^2 + 3x - 2)

= x^3(2x - 3) - (x^2 + 3x - 2)

Now, we can factor the second grouping by finding two numbers that multiply to -2 and add to 3. These numbers are 2 and -1. So we can rewrite the equation as:

x^3(2x - 3) - (x^2 + 3x - 2) = x^3(2x - 3) - (x - 2)(x + 1)

Now we have factored the equation completely, so we can set each factor equal to zero and solve for x:

x^3(2x - 3) - (x - 2)(x + 1) = 0

x^3(2x - 3) = (x - 2)(x + 1)

x = 0, or x = 2/3, or x = -1, or x = 2/3

Therefore, the solutions to the equation are x = 0, x = 2/3, and x = -1.