Nature of roots

Introduction Assume that α and β are the roots of the given quadratic equation. Sometimes we are given the relationship between the solutions of a quadratic equation and forced to reveal the condition, i.e., the relations between roots and coefficients a, b, and c of the quadratic equation.  Quadratic Equations Quadratic equations are polynomial formulae of […]

We rationalize the denominator to make any calculation on the rational number easy. When we rationalize the denominator in a fraction, we are removing any radical expressions from the denominator, such as square roots and cube roots. Rationalizing is the process of multiplying a surd by another surd of the same kind to produce a

When a rational number is expressed in standard form, it indicates the numerator and denominator have no common factors other than 1, and the denominator is a positive integer. Rational numbers are those that can be represented in the form p/q, where p and q are integers and q is not equal to zero. As

The term “contradiction” in mathematics refers to the situation when we have a proposition p that is true and it’s negation p that is also true. As an illustration, let us consider the concept of contradiction in the context of an example: Consider the following two statements: p and q. A coprime integer is represented

As implied by the names, poly means many and nominal means terms, therefore a polynomial is a number of phrases in many different forms. Polynomials are often composed of a sum or difference of variables and exponents, respectively. Each phrase in the polynomial represents one of the terms in the polynomial. Example of a polynomial

The polynomial division is the division of any two polynomials by a third polynomial. Polynomials can be divided between a monomial and a polynomial, between two monomials, or between two polynomials, depending on the situation. It is useful in mathematics when we need to divide two expressions of the algebraic form into two parts. Now,

A polynomial is an expression that contains constants and variables which is connected through basic operations of algebra. Variables are also known as indeterminates. The notation of a polynomial is p(x) where x represents the variable. For example: p(x)= .x²+3x-9. We will discuss degree of polynomial , polynomial equation , polynomial function , types of

In mathematics, a linear equation in two variables is defined as an equation in the form ax+by+c in which the variables are real numbers and the variables are not equal to zero. A linear equation in two variables has the form ax+by+c when the variables are real numbers. In contrast, when dealing with a pair

Nature of the Roots Before learning about the nature of the roots, firstly, we need to understand quadratic equations. A quadratic polynomial is a polynomial of degree two. A quadratic polynomial becoming equal to zero results in the formation of a quadratic equation. In mathematics, quadratic equations are an essential aspect of Algebra. Quadratic equations

Algebraic expressions are formed by letters or alphabets that can be used to express numbers without providing their real values. The constants and Variables can be combined in an algebraic expression. A coefficient is any value that is put before and multiplied by a variable. Algebraic expressions are divided into monomial, binomial, trinomial, and polynomial