Find the roots of the equation calculator

Q: How do you find roots of an equation?

The roots are calculated using the formula, x = (-b ± √ (b2 - 4ac) )/2a. Discriminant is, D = b2 - 4ac. If D > 0, then the equation has two real and distinct roots. If D < 0, the equation has two complex roots.

Q: How do you find complex roots on a calculator?

How to use the complex roots calculator?.

We can help you solve an equation of the form "ax2 + bx + c = 0"
Just enter the values of a, b and c below:

algebra/images/quadratic-solver.js

Is it Quadratic?

Only if it can be put in the form ax2 + bx + c = 0, and a is not zero.

The name comes from "quad" meaning square, as the variable is squared (in other words x2).

These are all quadratic equations in disguise:

In disguise	In standard form	a, b and c
x2 = 3x -1	x2 - 3x + 1 = 0	a=1, b=-3, c=1
2(x2 - 2x) = 5	2x2 - 4x - 5 = 0	a=2, b=-4, c=-5
x(x-1) = 3	x2 - x - 3 = 0	a=1, b=-1, c=-3
5 + 1/x - 1/x2 = 0	5x2 + x - 1 = 0	a=5, b=1, c=-1

How Does this Work?

The solution(s) to a quadratic equation can be calculated using the Quadratic Formula:

The "±" means we need to do a plus AND a minus, so there are normally TWO solutions !

The blue part (b2 - 4ac) is called the "discriminant", because it can "discriminate" between the possible types of answer:

when it is positive, we get two real solutions,
when it is zero we get just ONE solution,
when it is negative we get complex solutions.

Learn more at Quadratic Equations

Note: you can still access the old version here.

Example: 3x^2-2x-1=0

Step-By-Step Example

Learn step-by-step how to solve quadratic equations!

Example (Click to try)

Choose Your Method

There are different methods you can use to solve quadratic equations, depending on your particular problem.

Solve By Factoring

Example: 3x^2-2x-1=0

Complete The Square

Example: 3x^2-2x-1=0
(After you click the example, change the Method to 'Solve By Completing the Square'.)

Take the Square Root

Example: 2x^2=18

Quadratic Formula

Example: 4x^2-2x-1=0

About quadratic equations

Quadratic equations have an x^2 term, and can be rewritten to have the form: ax2+bx+c=0

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Quadratic Formula Calculator

What do you want to calculate?

Example: 2x^2-5x-3=0

Step-By-Step Example

Learn step-by-step how to use the quadratic formula!

Example (Click to try)

2x2−5x−3=0

About the quadratic formula

Solve an equation of the form ax2+bx+c=0 by using the quadratic formula:

−b±√b2−4ac

Quadratic Formula Video Lesson

Solve with the Quadratic Formula Step-by-Step [1:29]

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A polynomial is defined as a type of expression in which the exponents of the variable should be a whole number.

What is Roots Calculator?

'Roots Calculator' is an online tool that helps to calculate the roots of a given polynomial. Online Roots Calculator helps you to calculate the roots of a given polynomial in a few seconds.

Roots Calculator

NOTE: Enter a polynomial only in terms of x only.

How to Use Roots Calculator?

Please follow the steps below to find the roots of a given polynomial:

Step 1: Enter the polynomial in the given input boxes.
Step 2: Click on the "calculate" button to find the roots of a given polynomial.
Step 3: Click on the "Reset" button to clear the fields and solve for different polynomials.

How to Find Roots Calculator?

A polynomial with a degree of 1 is known as a linear polynomial

A polynomial with a degree of 2 is known as a quadratic polynomial.

A polynomial with a degree of 3 is known as a cubic polynomial.

A polynomial with a degree of 4 is known as a quartic polynomial.

A polynomial with a degree of 5 is known as a quintic polynomial.

A polynomial with a degree(n) greater than 5 is known as an nth degree polynomial.

A polynomial with any degree equates it to zero and finds the roots of a given polynomial.

The word "Quadratic" is derived from the word "Quad" which means square. In other words, a quadratic equation is an “equation of degree 2”

An equation of the form ax2 + bx + c = 0, where a ≠ 0 is called a quadratic equation and a, b, c are coefficients of the quadratic equation.

To solve the quadratic equation, we need to find the roots of a given quadratic equation, we use the discriminant formula given by:

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

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Solved Examples on Roots Calculator

Example1:
Solve the given linear equation 3x + 5 = 0
Solution:
3x + 5 = 0
3x = -5
x = -5 / 3
Example2:
Solve the quadratic equation x2 + 5x + 6 =0
Solution:
Given: a = 1, b = 5, c = 6
\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)
\(x = {-5 \pm \sqrt{5^2-24} \over 2}\)
\(x = {-4 \over 2}, {-6 \over 2}\)
\(x= {-2},{-3}\)
Example3:
Find roots of given polynomial x3 - 27 = 0
Solution:
x3 - 27 = 0
x3 = 27
x = 3

Show solution >

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Similarly, you can try the calculator to find the roots for the following:

2x3 + x - 3 = 0
x4 + 10x3 - 5x - 11 = 0

Polynomials
Linear equations
Quadratic equations

☛ Math Calculators:

How do you find roots of an equation?

The roots are calculated using the formula, x = (-b ± √ (b² - 4ac) )/2a. Discriminant is, D = b² - 4ac. If D > 0, then the equation has two real and distinct roots. If D < 0, the equation has two complex roots.