# Algebra

## Polynomials Class 9th

We have studied algebraic expressions in the previous classes and we know that algebraic expressions are mixed expressions of English alphabets and numeric values. Polynomials are also a special type of algebraic expression. The word ‘polynomial’ is made up of two Greek words “poly” and “nominal”. “Poly” means many and “nominal” means terms. Therefore, polynomial …

## Linear Equations in Two Variables Class 9th

Standard Form of Linear Equations in Two Variables ax + by + c = 0 Example – Write each of the following equations in the form ax + by + c = 0 and indicates the values of a, b, and c in each case: (i) 3x + 4y = 7      (ii) x – 5 …

## Pair of Linear Equations in Two Variables Class 10th

We are familiar with linear equations in two variables as we have studied them in previous classes. The linear equation having two variables is called the linear equation in two variables. In class 10th, we shall study the pair of linear equations in two variables, the solution of a pair of linear equations in two …

## Geometrical (Graphical) Meaning of the Zeroes of a Polynomial Class 10th

Introduction We know that if a polynomial is p(x) and R is it’s zero then p(R) = 0. It means the zeroes of every polynomial satisfy it. Let’s understand this with the help of geometrical or graphical representation. In class 10th, We shall study the geometrical representation of linear polynomials, quadratic polynomials, and cubic polynomials, …

## Linear Equations in One Variable Class 8th

Introduction We are familiar with algebraic expressions and equations because we have already studied these in the previous class. Algebraic expressions are mathematical expressions that have a combination of numbers and the English alphabet letters. In the equations, there is the equality sign (=) that is not used in algebraic expressions. Some examples of algebraic …

## Quadratic Formula (Shridharacharya Sutra) Class 10th

Introduction Quadratic Formula (Shridharacharya Sutra) – The quadratic formula is given by the great Indian mathematician Shridharacharya and is also known as Shridharacharya Sutra. This formula is used to solve the quadratic equation. x = –b ± √(b2 – 4ac)/2a Where, x = variable a, b, c = Coefficients of quadratic equation Derivation of Formula …

## Perfect the Square Method Class 10th

Perfect The Square Method (Complete The Square Method) Introduction In the Perfect the Square Method, we convert the quadratic equation into the perfect square form and then we take the square root to obtain the required roots. This method will be clear by the following examples. Examples Example – 1) Solve the quadratic equation 9×2 …

## Factorization Method Class 10th

Introduction In the Factorization Method, we factorize the quadratic equation and put each factor equal to zero and then find the values of x. These values of x are the solution of the quadratic equation and are called the roots of the quadratic equation. This can be understood by the following examples. Examples Example – …

Definition The polynomial in one variable (like x) with degree 2 is called Quadratic Equation. Examples – 2×2 + 3x + 5, x2 – 4x + 7, x2 + 8, 3×2 + 9x,…. etc. Standard Form of Quadratic Equation ax2 + bx + c = 0 Where a, b, and c are real numbers and …

## Relationship Between Zeroes and Coefficients of a Quadratic Polynomial Class 10th

Introduction We use the standard form of a quadratic polynomial to find the Relationship between Zeroes and Coefficients of a Quadratic Polynomial. We know the standard form of a quadratic polynomial is f(x) = ax2 + bx + c. Derivation of Formula Let α and β be the two zeroes of this polynomial. Then (x – …

## Division Algorithm, Remainder Theorem, and Factor Theorem Class 10th

Introduction Division Algorithm, Remainder Theorem, and Factor Theorem all three are related to Algebra. These three represent the relationship between the two functions. Division Algorithm If p(x) and g(x) are two such polynomials that the degree of p(x) is greater than g(x) and g(x) ≠ 0, and we divide p(x) by g(x) then we get two …

## Zeroes of the Polynomials Class 10th

Solving Polynomials Introduction To solve a polynomial, we put that polynomial equals zero (0) and find the value of the variable in it. Values of the variable are called zeroes or roots of the polynomial which depend on the degree of the polynomial. if the degree of the polynomial is 1 then there will be …

## Operations on Polynomials Class 10th

Introduction Operations on polynomials are the addition of polynomials, the subtraction of polynomials, the multiplication of polynomials, and the division of polynomials. ➤ Addition of polynomials ➤ Subtraction of polynomials ➤ Multiplication of polynomials ➤ Division of polynomials Addition of Polynomials When we add two or more polynomials then only like terms are added. it …

## Polynomials Class 10th

Introduction A polynomial word is made up of two Greek terms “poly” which means many and “nominal” which means terms So, a polynomial means many terms. Polynomials are the combined expression of variables, constants, and exponents (only whole numbers) with arithmetic expressions like addition, subtraction, multiplication, and division (division by only constant terms). Polynomials can …

## Sum of First n Terms of an Arithmetic Progression Class 10th

Introduction We know that there are n terms in an Arithmetic Progression (AP) and if we want the sum of the first n terms of an Arithmetic Progression then what should we do, we shall add all the terms of the AP but that will take more time to solve. Sometimes this method will not …

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