Quadratic Equation

Quadratic equations can be described as 2nd-degree expressions of algebra. These can be expressed in the px² + qx + r = 0. In this context, it should be mentioned that the word quadratic has come from the word quad. The meaning of the word quad is square. Simply stating a 2nd-degree equation is called a quadratic equation. The quadratic equation is used for several different purposes. Further, it can be stated that quadratic equations are 2nd degree in the variable x which gives two values of x. These 2 values of x are often referred to as the roots of the equation.

Quadratic Equation Definition

A particular algebraic equation in the 2nd degree of x is defined as a quadratic equation. The standard form of a quadratic equation is given by px² + qx + r = 0, where p and q are defined as the coefficients, x is defined as the variable, and r is defined as the constant term. The 1st condition that is necessary to become a quadratic equation is that the coefficient of the term x² must be non-zero. This means p ≠ 0. To specifically write an equation in the standard form of a quadratic equation, the term x² is written first. This is followed by the term x along with its coefficient. After this, the constant term is written in the equation. The numerical values of p, q, and r are not normally written in the form of decimals or fractions. These are written in the form of integral values.

Quadratic Equation Formula

Quadratic equation Formula is the simplest way through which the roots of a quadratic equation can be identified. Many quadratic equations are difficult to factorise. In these cases, the formula of a quadratic equation can be used for finding the roots of these equations quickly. If the roots of a quadratic equation are calculated with the help of the formula of the quadratic equation then they can be used to find the sum of the calculated roots as well as the product of the calculated roots of the given quadratic equation. The 2 roots in the formula of the quadratic equation are presented in the form of a particular expression. The negative sign, as well as the positive sign within the formula, can be used alternatively to obtain 2 roots within the equation.

If the 2nd degree equation or quadratic equation be taken as px² + qx + r = 0, then the formula for the quadratic equation is given as [- q ± √ (q² – 4pr)] / 2p

Roots of Quadratic Equation

The roots of the quadratic equation are defined as the answers of x that are obtained through the calculation of the quadratic equation. The roots of the quadratic equation can be the same or can also be different. The 2 answers of x or the 2 roots are denoted by the standard notations ‘β’ that is Beta and ‘α’ that is alpha. The roots of a quadratic equation are often referred to as the zeros within the equation. Within the discussion of the roots of the quadratic equation, several aspects are vital which have been outlined in the following.

Nature of the roots of quadratic equation: Without actual computation of the roots of a quadratic, the nature of its roots can be identified. This can be done by calculating the discriminant, which is included within the quadratic equation formula. The value (q² – 4pr) is defined as the discriminant within a quadratic equation. This discriminant value is denoted by ‘D’. Based on this discriminant value the nature of the roots can be estimated. If the value of D is greater than 0 then, roots are distinct as well as real. If the value of D is equal to 0 then, roots are equal as well as real. Finally, if the value of D is greater than 0 then the quadratic equation roots either do not exist or are imaginary.

Conclusion

The core topic that the article has been written on is the quadratic equation which is a vital topic within quantitative aptitude. Within this core topic, several subtopics have been discussed including the. The subtopics that have been mainly analysed are the definition of a quadratic equation, quadratic equation formula, and roots of quadratic equation.