solve the following equations:- x - 1 x - 2 + x - 3 x - 4 = 3 1 3

A number α is a root (or solution) of a quadratic equation a x 2 + b x + c = 0 if it satisfies the equation i.e. a α 2 + b α + c = 0 . Method to solve a quadratic equation by factorisation is as follows: 1 . Clear all fractions and write the equation in the form a x 2 + b x + c = 0 . 2 . Factorise the left hand side into product of two linear factors. 3 . Put each linear factor equal to zero and solve the resulting linear equations. The given equation is: x - 1 x - 2 + x - 3 x - 4 = 3 1 3 ⇒ ( x - 1 ) ( x - 4 ) + ( x - 2 ) ( x - 3 ) ( x - 2 ) ( x - 4 ) = 10 3 ⇒ x 2 - 5 x + 4 + x 2 - 5 x + 6 x 2 - 6 x + 8 = 10 3 ⇒ 2 x 2 - 10 x + 10 x 2 - 6 x + 8 = 10 3 ⇒ 10 x 2 - 60 x + 80 = 6 x 2 - 30 x + 30 ⇒ 10 x 2 - 60 x + 80 - 6 x 2 + 30 x - 30 = 0 ⇒ 4 x 2 - 30 x + 50 = 0 ⇒ 2 x 2 - 15 x + 25 = 0 ⇒ 2 x 2 - 10 x - 5 x + 25 = 0 ⇒ 2 x ( x - 5 ) - 5 ( x - 5 ) = 0 ⇒ ( x - 5 ) ( 2 x - 5 ) = 0 ⇒ x - 5 = 0 & 2 x - 5 = 0 ⇒ x = 5 & x = 5 2 ∴ x = 5 2 , 5 are roots of the given equation.

solve the following equations:- 6 x - 2 x - 1 = 1 x - 2

A number α is a root (or solution) of a quadratic equation a x 2 + b x + c = 0 if it satisfies the equation i.e. a α 2 + b α + c = 0 . Method to solve a quadratic equation by factorisation is as follows: 1 . Clear all fractions and write the equation in the form a x 2 + b x + c = 0 . 2 . Factorise the left hand side into product of two linear factors. 3 . Put each linear factor equal to zero and solve the resulting linear equations. The given equation is: 6 x - 2 x - 1 = 1 x - 2 ⇒ 6 x - 6 - 2 x x ( x - 1 ) = 1 x - 2 ⇒ 6 x - 6 - 2 x x 2 - x = 1 x - 2 ⇒ ( 4 x - 6 ) ( x - 2 ) = x 2 - x ⇒ 4 x 2 - 8 x - 6 x + 12 = x 2 - x ⇒ 4 x 2 - 14 x + 12 - x 2 + x = 0 ⇒ 3 x 2 - 13 x + 12 = 0 ⇒ 3 x 2 - 4 x - 9 x + 12 = 0 ⇒ x ( 3 x - 4 ) - 3 ( 3 x - 4 ) = 0 ⇒ ( 3 x - 4 ) ( x - 3 ) = 0 ⇒ 3 x - 4 = 0 & x - 3 = 0 ⇒ x = 4 3 & x = 3 ∴ x = 4 3 , 3 are roots of the given equation.

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Understanding ICSE Mathematics Class 9>Algebra>Chapter 7 - Quadratic Equations>Chapter Test

M L Aggarwal Solutions for Exercise 3: Chapter Test

Author:M L Aggarwal

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Exercise 3: Chapter Test

Attempt the practice questions from Exercise 3: Chapter Test with hints and solutions to strengthen your understanding. Understanding ICSE Mathematics Class 9 solutions are prepared by Experienced Embibe Experts.