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
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
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
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
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
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
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
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
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