Question

5x^4-9x^3-2x^2+4x-8=0

Answer 1

Ответ:

х1=-1

х1=2

Объяснение:

в фото............

Answer 2

To solve the equation 5x^4 - 9x^3 - 2x^2 + 4x - 8 = 0, we can use various methods, such as factoring, using the Rational Root Theorem, or using numerical methods like graphing or numerical approximation algorithms. However, this equation doesn't appear to have a straightforward factorization, and its roots might not be easy to find analytically.

One way to approach this is by using numerical methods. Let's use a numerical approximation algorithm like the Newton-Raphson method to find an approximate solution for this equation.

The Newton-Raphson method uses the formula:

x1 = x0 - f(x0) / f'(x0)

where: x1 is the next approximation, x0 is the current approximation (initial guess), f(x0) is the value of the function at x0, f'(x0) is the derivative of the function at x0.

Let's start with an initial guess, and then we'll iterate through the Newton-Raphson formula until we find a reasonably accurate solution.

Let's take x0 = 1 as the initial guess:

Iteration 1: x1 = x0 - f(x0) / f'(x0) x1 = 1 - (5(1)^4 - 9(1)^3 - 2(1)^2 + 4(1) - 8) / (4(5(1)^3) - 3(9(1)^2) - 2(2(1)) + 4) x1 = 1 - (5 - 9 - 2 + 4 - 8) / (20 - 27 - 4 + 4) x1 = 1 - (-10) / (-7) x1 = 1 + 10/7 x1 = 17/7 ≈ 2.429

Iteration 2: Using x0 = 17/7 as the new approximation: x1 = x0 - f(x0) / f'(x0) x1 = 17/7 - (5(17/7)^4 - 9(17/7)^3 - 2(17/7)^2 + 4(17/7) - 8) / (4(5(17/7)^3) - 3(9(17/7)^2) - 2(2(17/7)) + 4) x1 ≈ 2.248

Iteration 3: Using x0 = 2.248 as the new approximation: x1 ≈ 2.239

We can continue these iterations until we reach a satisfactory level of accuracy. However, it's important to note that this method may not converge for all initial guesses or may converge to different roots if the equation has multiple solutions.

Alternatively, you can use numerical methods in software like MATLAB, Python (using libraries like NumPy), or WolframAlpha, which will provide more accurate and efficient solutions.