Find the quadratic equation given the roots calculator

This Solver (Find A Quadratic Equation Given The Solutions) was created by by jim_thompson5910(35256)

Find A Quadratic Equation Given The Solutions

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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

1. Example1:
   Solve the given linear equation 3x + 5 = 0
   Solution:
   3x + 5 = 0
   3x = -5
   x = -5 / 3

2. Example2:

   Solve the quadratic equation x2 + 5x + 6 =0

   Solution:

   Given: a = 1, b = 5, c = 6

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

   \(x = {-5 \pm \sqrt{5^2-24} \over 2}\)

   \(x = {-4 \over 2}, {-6 \over 2}\)

   \(x= {-2},{-3}\)

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

☛ Related Articles:

• Polynomials
• Linear equations
• Quadratic equations

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