CBSE Class 10 Quadratic Equations Important Formulas and concepts for exams

CBSE Class 10 Quadratic Equations Important Formulas and concepts for exams. There are many more useful educational material which the students can download in pdf format and use them for studies. Study material like concept maps, important and sure shot question banks, quick to learn flash cards, flow charts, mind maps, teacher notes, important formulas, past examinations question bank, important concepts taught by teachers. Students can download these useful educational material free and use them to get better marks in examinations.  Also refer to other worksheets for the same chapter and other subjects too. Use them for better understanding of the subjects.

POLYNOMIALS

An algebraic expression of the form p(x) = a₀ + a₁x + a₂x² + a₃x³+ …………….a_nxⁿ, where a ≠  0, is called a polynomial in variable x of degree n.

Here, a₀, a₁, a₂, a₃, ………,an are real numbers and each power of x is a non-negative integer. e.g. 3x²  – 5x + 2 is a polynomial of degree 2.

3√ 2 x + is not a polynomial.

• If p(x) is a polynomial in x, the highest power of x in p(x) is called the degree of the polynomial p(x). For example, 4x + 2 is a polynomial in the variable x of degree 1, 2y²– 3y + 4 is a polynomial in the variable y of degree 2,

 • A polynomial of degree 0 is called a constant polynomial.

  • A polynomial p(x) = ax + b of degree 1 is called a linear polynomial.

  • A polynomial p(x) = ax² + bx + c of degree 2 is called a quadratic polynomial.

  • A polynomial p(x) = ax³ + bx² + cx + d of degree 3 is called a cubic polynomial.

  • A polynomial p(x) = ax⁴+ bx³ + cx² + dx + e of degree 4 is called a bi-quadratic polynomial.

QUADRATIC EQUATION

A polynomial p(x) = ax² + bx + c of degree 2 is called a quadratic polynomial, then p(x) = 0 is known as quadratic equation.

e.g. 2x² – 3x + 2 = 0, x² + 5x + 6 = 0 are quadratic equations.

METHODS TO FIND THE SOLUTION OF QUADRATIC EQUATIONS

Three methods to find the solution of quadratic equation:

1. Factorisation method

2. Method of completing the square

3. Quadratic formula method

FACTORISATION METHOD

Steps to find the solution of given quadratic equation by factorisation

  • Firstly, write the given quadratic equation in standard form ax² + bx + c = 0.

  • Find two numbers a and b such that sum of a and b is equal to b and product of a and b is equal to ac.

  • Write the middle term bx as αx+βx and factorise it by splitting the middle term and let factors are (x + p) and (x + q) i.e. ax²+ bx + c = 0=›(x + p)(x + q) = 0

 • Now equate reach factor to zero and find the values of x.

 • These values of x are the required roots/solutions of the given quadratic equation.

METHOD OF COMPLETING THE SQUARE

Steps to find the solution of given quadratic equation by Method of completing the square:

  • Firstly, write the given quadratic equation in standard form ax² + bx + c = 0.

  • Make coefficient of x² unity by dividing all by a then we get x²+b/ax+c/a=0

  • Shift the constant on RHS and add square of half of the coefficient of x i.e. (b/2a)² on both sides.

Please click the link below to download CBSE Class 10 Quadratic Equations Important Formulas and concepts for exams.