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 …
We are familiar with linear equations in two variables as we have studied them in the 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 …
Pair of Linear Equations in Two Variables Class 10th Read More »
Introduction We know that if a polynomial is p(x) and R is it’s zero then p(R) = 0. It means 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 polynomial, quadratic polynomial, cubic polynomial, and also …
Geometrical (Graphical) Meaning of the Zeroes of a Polynomial Class 10th Read More »
Introduction We are familiar with algebraic expressions and equations because we have already studied these in the previous class. Algebraic expressions are the mathematical expressions that have the 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 …
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 …
Quadratic Formula (Shridharacharya Sutra) Class 10th Read More »
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 …
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 …
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 – …
Relationship Between Zeroes and Coefficients of a Quadratic Polynomial Class 10th Read More »
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 …
Division Algorithm, Remainder Theorem, and Factor Theorem Class 10th Read More »
