## Nature of Roots of Quadratic Equations

The nature of roots of quadratic equations is determined by whether the roots are real, complex, they are equal, or unequal. The nature of the roots of a quadratic equation can be determined by the discriminant of the equation. Let’s learn about that in this post. What are Roots of a Quadratic Equation An equation … Read more

## Solve x^6-1=0 and Find the Roots

The solutions of x6=1 (x to the power 6 equals 1) are given by x= 1, -1, (-1+√3i)/2, (-1-√3i)/2, (1+√3i)/2, and (1-√3i)/2, where i = √-1 is an imaginary complex number. In this post, we will learn how to find the roots of x^6=1. Solutions of x6=1 To solve the given equation x6=1, we need … Read more

## Solution of x^4=1 | Roots of x^4=1

The solutions of x4=1 (x to the power 4 equals 1) are given by x= 1, -1, i, and -i where i=√-1 is the imaginary complex number. In this post, we will learn how to find the roots of x4=1. Solutions of x4=1 To solve the given equation x4=1, we need to follow the below … Read more

## x^3=1 Solution | x^3=1 Roots

The solutions of x3=1 (x cubed equals 1) are given by x= 1, ω, and ω2 where ω = (-1+√3i)/2 is the complex number. In this post, we will learn how to find the root of x3=1. Solutions of x3=1 The given equation is x3=1. Step 1: Apply the formula of a3-b3. ⇒ x3 -1 … Read more

## How to Solve Quadratic Equation

There are many techniques for how to solve quadratic equations. For example, we can solve a quadratic equation by factoring or directly using the quadratic formula. In this post, we will learn about the same. Solving Quadratic Equations using Factoring  To solve a quadratic equation using the factoring method, we will follow the below steps … Read more

## Factorise x^4+4x^2+3 | How to Solve x^4+4x^2+3=0

The equation x4+4×2+3=0 is a bi-quadratic equation. In this post, we will first factorise x4+4×2+3 and then solve the equation x4+4×2+3=0. How to Factorise x4+4×2+3 Question: Factorize x4+4×2+3. Solution: To factorize x4+4×2+3, our aim is to express it in the form of a2-b2. For that, we need to add and subtract 1 to both sides. … Read more

## How to Solve Linear Equations

A linear equation in one variable is always of the form ax+b=c, where a, b, and c are constants. Linear equations are also known as simple equations. In this post, we will learn how to solve linear equations with examples. ax+b=c Put c=0. Then ax+b = 0 ⇒ ax = -b This is an equation … Read more

## How to Factorise x^2+25 | Solve x^2+25=0

In this post, we will learn how to factorise the quadratic algebraic expression x2+25, then solve the quadratic equation x2+25=0. How to Factorise x2+25? Answer: The factorization is given by x2+25 = (x-5i)(x+5i), where i = √-1 is an imaginary complex number. Solution: To factorise the expression x2+25, we first write the expression in the … Read more

## How to Factorise and Solve x^4+x^2+1=0

In today’s article, we will first factorize the expression x4+x2+1, and then we will solve the bi-quadratic equation x4+x2+1=0. How to Factorise x4+x2+1 Answer: The factorisation of x4+x2+1 is given by x4+x2+1 = (x2-x+1)(x2+x+1). Solution: At first, we will add and subtract x2 to the given expression. x4+x2+1 = (x4+x2+1) + x2 – x2 = … Read more