Introduction to Rational Zeros Calculator:
Rational Zeros Calculator is an online tool that helps you find the rational roots of algebraic equations using the rational zero theorem.
Rational root theorem calculator computes the polynomial whose exponential integer value gives the rational zeros value although the polynomial does not have the rational zeroes.
What are Rational Zeros?
Rational Zeros are defined as polynomial functions of the exponents that have integer degrees with coefficients in descending order.
All rational zero is present in the form ± p q, in which p is a factor of the constant term and q is a factor of the leading coefficient that gives all the possible rational zeros roots.
Formula Behind Rational Zero Theorem Calculator:
The rational zeros formula used by Rational Zeros Calculator has a polynomial equation with constant coefficients a and variables whose exponential power is arranged from a higher degree to a lower degree.
$$ P(x) \;=\; a_n x^n + a_{n-1} x^{n-1} + … + a_1 x + a_0 \; where \; ( a_n \neq 0) $$
Working Process of Rational Root Theorem Calculator:
Rational root calculator uses the rational zero theorem to get all possible rational roots of polynomial equations. It provides you step by step solution of rational theorem problems.
When you add the polynomial equation to the rational zeros theorem calculator, it takes the coefficient of leading term or constant values.
Rational numbers are in the form of p/q in which p is a constant and q is the leading value. Rational zero calculator writes down all the possible values in the form of p/q using their factors terms and all the repeated terms are not added.
After finding all possible roots, rational roots calculator adds these all one by one in f(x) to find (x) = 0. All these roots do not give the zero value but more than one can give rationals zero. If all roots do not provide f(x) ≠ 0 then the given polynomial has no rational root values. You can observe the given example of rational roots and understand how the rational zeros calculator works.
Solved Example of Rational Zeros:
Let's see an example of polynomial equation problem with a solution to understand how to solve rational zeros problems manually.
Example:
Find the rational zeros of the following using the rational zero theorem:
$$ f(x) \;=\; 2x^3 + x^2 - 4x + 1 $$
Solution:
Using the formula,
$$ \frac{p}{q} \;=\; \frac{factor\;of\;constant\;term}{factor\;of\;leading\;coefficient} $$
$$ \frac{factor\;of\;1}{factor\;of\;2} $$
We get the factor of 1 is +1,-1, and the factor of 2 is +1,-1,+2,-2.
Possible roots for p/q are +1,-1, or -½,+½. Then substitute these roots in the given equation.
$$ f(-1) \;=\; 2(-1)^3 + (-1)^2 - 4(-1) + 1 \;=\; 4 $$
$$ f(1) \;=\; 1(1)^3 + (1)^2 - 4(1) + 1 \;=\; 0 $$
$$ f \biggr(-\frac{1}{2} \biggr) \;=\; 2 \biggr( -\frac{1}{2} \biggr)^3 + \biggr( -\frac{1}{2} \biggr)^2 - 4 \biggr( -\frac{1}{2} \biggr) + 1 \;=\; 3 $$
$$ f \biggr( \frac{1}{2} \biggr) \;=\; 2 \biggr( \frac{1}{2} \biggr)^3 + \biggr( \frac{1}{2} \biggr)^2 - 4 \biggr( \frac{1}{2} \biggr) + 1 \;=\; -\frac{1}{2} $$
How to Use Rational Zeros Calculator?
Rational zero theorem calculator has a user-friendly interface so that you can use it to calculate the algebraic function.
Before giving an input to rational zero calculator, you must follow given instructions so that you can avoid any type of trouble. These steps are:
- Choose the highest degree of polynomial equation.
- Enter all the coefficients in the relevant field.
- Recheck your algebraic function before clicking the calculate button.
- Click the “Calculate” button to get the result of a polynomial equation.
- If you are trying our rational root theorem calculator first time then use the load example option.
- Tap on the “Recalculate” option to get a new page for solving more rational zeros problems.
Output from Rational Zeros Theorem Calculator:
Rational zeros calculator gives you the solution in positive or negative roots when you add the algebraic function. It provides you solutions in steps. It contain as
- Result option gives you a solution in the form of roots for a polynomial equation.
- Possible step provides you all the steps where a complete procedure is given for finding the positive or negative root of a polynomial equation.
Benefits of Rational Zero Calculator:
Rational roots calculator gives you millions of benefits whenever you use it to calculate the polynomial equation problem of an algebraic function. These benefits are:
- It takes time to calculate the root of rational zeros manually but our rational zero theorem calculator saves time and give instant solution.
- It is a free-of-cost tool so you can use it for free to find the polynomial equation of all the possible positive or negative roots.
- Rational root theorem calculator is a versatile tool that allows you to solve polynomial higher-degree equations and gives solutions in the form of rational zero roots.
- You can use this rational zeros theorem calculator for practicing rational zeros theorem problems.
- Rational zeros calculator provides you with accurate solutions whenever you use it to find the rational zero roots.
