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# Rational Zeros Calculator

Enter the function and click calculate button to calculate the actual rational roots using the rational zeros calculator

## Rational Zeros Calculator

Rational zeros calculator is used to find the actual rational roots of the given function. This possible rational zeros calculator evaluates the result with steps in a fraction of a second.

## What is the Rational zeros theorem?

The rational root theorem is a fundamental theorem in algebraic number theory and is used to determine the possible rational roots of a polynomial equation.

It states that if a polynomial equation has a rational root, then that root must be expressible as a fraction **p/q**, where **p **is a divisor of the leading coefficient and **q** is a divisor of the constant term.

The theorem is important because it provides a way to simplify the process of finding the roots of a polynomial equation. For example, suppose we have a polynomial equation

**f(x) = ax ^{n }+ bx^{(n-1)} + ... + c**

The theorem states that any rational root of this equation must be of the form **p/q**, where

and **p **divides c`q divides a`

. This means that we can start by testing all the possible rational numbers of this form, instead of having to test every possible real number.

## How to find all the zeros of polynomials?

We have to follow some steps to find the zeros of a polynomial:

**List the factors**of the constant term and the coefficient of the leading term.- Now divide factors of the leadings with factors of the constant.
- Remove the duplicated terms.
- If we put the zeros in the polynomial, we get the remainder equal to zero.

## How to calculate rational zeros?

**Example:**

Evaluate the polynomial **P(x)= 2x ^{2 }- 5x - 3.**

**Solution:**

**Step 1:** First we have to make the factors of constant **3** and leading coefficients **2**.

`Factors of 3 = +1, -1, 3, -3`

`Factors of 2 = +1, -1, 2, -2`

**Step 2: **Divide the factors of the constant with the factors of the leading term and remove the duplicate terms.

Possible rational roots: 1/2, 1, 3/2, 3, -1, -3/2, -1/2, -3

**Check 1:** Divide **2x ^{2 }- 5x - 3 **by

**x- 1**.

P(1) = 2(1)^{2} - 5(1) - 3

`P(1) = -6`

**Check 2:** Divide **2x ^{2 }- 5x - 3 **by

**x - 3**.

P (3) = 2(3)^{2} - 5(3) - 3

`P (3) = 0 `

**Check 3:** Divide **2x ^{2 }- 5x - 3 **by

**x - 3/2**.

P (3/2) = 2(3/2)^{2} - 5(3/2) - 3

`P (3/2) = -6`

**Check 4:** Divide **2x^2-5x-3 **by **x+1/2**.

P (-1/2) =2(-1/2)^2 -5(-1/2)-3

`P (-1/2) = 0`

**Check 5: **Divide** 2x ^{2 }- 5x - 3 **by

**x+3/2**.

P (3/2) = 2(3/2)^{2} - 5(3/2) - 3

`P (3/2) = 9`

**Check 6: **Divide **2x ^{2 }- 5x - 3** by

**x- 1/2**.

P (1/2) = 2(1/2)^{2 }- 5(1/2) - 3

`P (1/2) =-5`

**Check 7: **Divide **2x ^{2 }- 5x - 3** by

**x+3**.

P (3) = 2(3)^{2} - 5(3) - 3

`P (3) = 30`

**Check 8:** Divide **2x ^{2 }- 5x - 3 **by

**x+1**.

P (-1) = 2(-1)^{2} - 5(-1) - 3

`P (-1) = 5`

**Actual rational roots are 3,-1/2**