# Roots of Polynomials Calculator

Use * to indicate multiplication between coefficients and variables. For example, write 4*x or 5*x, instead of 4x or 5x.

**Answer:**

**Examples:**

- To write \(x^2+2x+5\), enter x^2+2*x+5.
- To write \(9x^2-18x+17\), enter 9*x^2-18*x+17.

This calculator allows you to find the roots of a polynomial. If the polynomial is valid and entered correctly, the calculator will return all its roots, including imaginary roots.

## How to use the calculator of roots of polynomials?

**Step 1:** Enter the polynomial in the corresponding input box. For the polynomial to be recognized correctly, use * to indicate multiplication between variables and coefficients. For example, enter 5*x or 2*x^2, instead of 5x or 2x^2.

**Step 2:** Click “Solve” to get all the roots of the polynomial.

**Step 3:** If the polynomial was entered correctly, its solutions, along with the original polynomial, will be displayed at the bottom.

## How to enter polynomials in the calculator?

To enter polynomials correctly, we have to use * to indicate multiplication between variables and coefficients. That is, instead of entering 5x or 2x, we must enter 5*x or 2*x.

Also, we must use the ^ sign to indicate an exponent. For example, to indicate \(x^2\), we have to enter x^2. The following are some examples of how to input polynomials:

- To write \(x^2+4x+2\), enter x^2+4*x+2.
- To write \(2x^2-11x+7\), enter 2*x^2-11*x+7.
- To write \(\frac{1}{3}x^2-\frac{1}{2}x+2\), enter 1/3*x^2-1/2*x+2.

In the last example, we can see that we can also enter fractional coefficients. As long as it is entered correctly, any valid polynomial can be solved.

## What if the polynomial has no real roots?

If the polynomial has no real roots, the calculator will return its imaginary roots. This means that we can find all the roots of a polynomial according to the fundamental theorem of algebra.

## What are the roots of polynomials?

The roots of a polynomial are the values of a variable, for which the polynomial is equal to zero. If *a* is a root of the polynomial *p*(*x*), then *p*(*a*)=0.

The roots of a polynomial can be found using factoring techniques. However, for polynomials of degrees greater than 3 or 4, finding polynomial roots manually can be tedious. Therefore, using a calculator like the one shown above can be very helpful.

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