Maths Class 11 Chapter 5 Notes

• Our comprehensive Maths Class 11 Chapter 5 Notes will ensure you're fully prepared for your exams.
• Definition of inconsistent equation
• Definition of a fraction, partial fractions with examples, conditional equations with examples, identity with examples, rational fraction with examples.
• Definition of proper rational fraction and definition of improper rational fraction with examples
• Solution of each question in Exercise 5.1 in 1st year Mathematics of the Punjab Textbook Boards.
• Solution of each question in Exercise 5.2 in 1st year Mathematics of the Punjab Textbook Boards.
• Solution of each question in Exercise 5.3 in 1st year Mathematics of the Punjab Textbook Boards.
• The factor x2 - 5x + 6 in the denominator can be factorized and its factors are x - 3 and x - 2.
• a) the denominator of A is x - 1, and the value of A has been found by putting x - 1 = 0 i.e ;x = 1;
• b) the denominator of B is x - 2, and the value of B has been found by putting x - 2 = 0 i.e., x = 2 ; and
• c) the denominator of C is x - 3, and the value of C has been found by putting x - 3 = 0 i.e.,x = 3.
• when Q (x) contains non-repeated irreducible quadratic factor. Deinition: A quadratic, factor is irreducible if it cannot be written as the product of two linear factors with real coeicients. For example, x2 + x + 1 and x2+ 3 are irreducible quadratic factors. If the polynomial Q x( ) contains non-repeated irreducible quadratic factor then P (x)  / Q (x) may be written as the identity having partial fractions of the form: 2Ax Bax bx c ++ + where A and B the numbers to be found. The method is explained by the following examples:
• Resolution of a Rational Fraction P(x) / Q (x) into Partial Fractions following are the main points of resolving a rational fraction P(x) / Q (x) into partial fractions:
• i) The degree of P(x) must be less than that of Q(x). If not, divide and work with the remainder theorem.
• ii) Clear the given equation of fractions.
• iii) Equate the coeicients of like terms (powers of x).
• iv) Solve the resulting equations for the coeicients.
• Deinition: A quadratic, factor is irreducible if it cannot be written as the product of two linear factors with real coeicients. For example, x2+ x + 1 and x2+ 3 are irreducible quadratic factors. 
• If the polynomial Q(x) contains non-repeated irreducible quadratic factor then  P(x) / Q (x) may be written as identity having partial fractions.
• Rational Fraction We know that p / q where p, q U Z and q ≠ 0 is called a rational number. Similarly, the quotient of two polynomial P(x) / Q (x) where Q x( ) 0, ≠ with no common factors, is called a Rational Fraction. A rational fraction is of two types: 
• Proper Rational Fraction: A rational fraction  P(x) / Q (x) is called a Proper Rational Fraction if the degree of the polynomial P(x) in the numerator is less than the degree of the polynomial Q (x) in the denominator.
• Improper Rational Fraction:  A rational fraction P(x) / Q (x) is called an Improper Rational Fraction if the degree of the polynomial P(x) in the numerator is equal to or greater than the degree of the polynomial Q (x) in the denominator.