# Polynomial equation solver

# Polynomial equation solver

**To solve a polynomial equation, you can use a polynomial equation solver. Here are the steps to use a polynomial equation solver:**

- Enter the coefficients of the polynomial in the correct order, from highest degree to lowest degree.
- Enter the value of the variable that you want to solve for.
- Click the “Calculate” button or equivalent option.
- The solution(s) to the polynomial equation will be displayed.

**Alternatively, you can solve a polynomial equation manually by following these steps:**

- Write the polynomial equation in standard form, with the terms in descending order of degree.
- Factor the polynomial if possible.
- Set each factor equal to zero and solve for the variable.
- The solutions to the polynomial equation are the values of the variable that make the polynomial equal to zero.

Here’s an example to illustrate how to use a polynomial equation solver:

Suppose you have the polynomial equation 3x^3 – 4x^2 + 5x – 2 = 0.

**To solve this polynomial equation, you would follow these steps:**

- Enter the coefficients of the polynomial in the correct order: 3, -4, 5, -2.
- Enter the value of the variable that you want to solve for.
- Click the “Calculate” button or equivalent option.
- The solutions to the polynomial equation will be displayed.

**Alternatively, you could also factor this polynomial equation as:**

3x^3 – 4x^2 + 5x – 2 = (x – 1)(3x^2 – x + 2)

**Then, you would set each factor equal to zero and solve for the variable:**

x – 1 = 0 or 3x^2 – x + 2 = 0

Solving for x in each equation, we get:

x = 1 or x = (-1 ± √(1 – 4(3)(2))) / (2(3)) x = 1 or x = (-1 ± i√23) / 6

So the solutions to the polynomial equation are x = 1, x ≈ 0.224 + 0.813i, and x ≈ 0.224 – 0.813i.