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 in no time.
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 zero theorem calculator uses the rational zero theorem to get all possible rational roots of polynomial equations.
Our rational root calculator provides you with a complete procedure so that you get a clear idea about how its backend works and ensures you get the exact solution.
You need to 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 and find all the possible common factors of p and q 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 not added.
After finding all possible roots rational roots calculator adds all these roots one by one in f(x) to find (x)=0 for rational zeros. All these roots do not give the zero value but more than one may 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 know the workings of the Rational Zeros Calculator.
Solved Example of Rational Zeros
Let's see an example of polynomial equation problem with a solution and you will 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 in less than a minute.
Before adding the input value to the rational zero calculator, you must follow some instructions so that you can avoid any type of trouble in the evaluation process. These steps are:
- Choose the highest degree of polynomial equation
- Enter all the coefficients in the relevant field.
- Recheck your algebraic function before clicking on the calculate button.
- Click the “Calculate” button to get the desired result of a polynomial equation
- If you first time try our rational root theorem calculator then you can use the load example that gives you better clarity about its working procedure.
- 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 real roots when you add the algebraic function to it. It provides you with solutions in a step-wise process. It may contain as
- Result option gives you a solution in the form of roots for a polynomial equation
- Possible step provides you with 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:
- Rational zero theorem calculator takes time to calculate the root of rational zeros of polynomials when you do work manually but our tool saves time that you consume from doing lengthy calculations
- 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 real roots
- Rational root theorem calculator is a versatile tool that allows you to solve various types of polynomial higher-degree equations and gives solutions in the form of rational zero roots
- You can use this rational zeros theorem calculator for practice to get familiar with the concept of rational zeros using the rational zero theorem.
- Rational Zeros Calculator provides you with accurate solutions every time whenever you use it to find the rational zero roots calculation making it a trustworthy tool.
