Solve the quadratic equation by completing the square: 3 x 2 + 10 x + 7 3 = 0

Given equation: 3 x 2 + 10 x + 7 3 = 0 Dividing the above equation by 3 , we get x 2 + 10 3 x + 7 = 0 ⇒ x 2 + 10 3 x = - 7 [Transposing constant term to RHS] Adding 5 3 2 both sides, we get ⇒ x 2 + 2 x 5 3 + 5 3 2 = - 7 + 5 3 2 In above equation, LHS is of the form a 2 + 2 a b + b 2 which is the identity of ( a + b ) 2 ⇒ x + 5 3 2 = - 7 + 25 3 Subtracting the terms in RHS using LCM, we get ⇒ x + 5 3 2 = 4 3 ⇒ x + 5 3 = ± 2 3 ⇒ x = - 5 3 + 2 3 = - 5 + 2 3 = - 3 3 × 3 3 = - 3 or x = - 5 3 - 2 3 = - 5 - 2 3 = - 7 3 Hence, x = - 3 and x = - 7 3 are the roots of the given equation.

Solve, by completing the square: x 2 - 2 + 1 x + 2 = 0

Given equation: x 2 - 2 + 1 x + 2 = 0 Transposing constant term to RHS, we get x 2 - 2 + 1 x = - 2 Multiplying and dividing 2 to 2 + 1 x , we get x 2 - 2 x 2 + 1 2 = - 2 Adding 2 + 1 2 2 on both sides, we get ⇒ x 2 - 2 x 2 + 1 2 + 2 + 1 2 2 = - 2 + 2 + 1 2 2 In above equation, LHS is of the form a 2 - 2 a b + b 2 which is the identity of ( a - b ) 2 ⇒ x - 2 + 1 2 2 = - 2 + 2 + 2 2 + 1 4 Subtracting the terms in RHS using LCM, we get x - 2 + 1 2 2 = - 4 2 + 2 + 2 2 + 1 4 ⇒ x - 2 + 1 2 2 = 2 - 2 2 + 1 4 The numerator in the RHS 2 - 2 2 + 1 is of the form 2 2 - 2 × 2 × 1 + 1 2 = 2 - 1 2 ⇒ x - 2 + 1 2 2 = 2 - 1 2 2 ⇒ x - 2 + 1 2 = ± 2 - 1 2 ⇒ x = 2 + 1 ± 2 - 1 2 ⇒ x = 2 + 1 + 2 - 1 2 or x = 2 + 1 - 2 - 1 2 ⇒ x = 2 2 2 = 2 or x = 2 2 = 1 Hence, x = 2 and x = 1 are the roots of the given equation.

E M B I B E

Modern's abc+ of Mathematics for Class 10>Chapter 4 - Quadratic Equations>EXERCISE

J P Mohindru and Bharat Mohindru Solutions for Chapter: Quadratic Equations, Exercise 4: EXERCISE

Author:J P Mohindru & Bharat Mohindru

J P Mohindru Mathematics Solutions for Exercise - J P Mohindru and Bharat Mohindru Solutions for Chapter: Quadratic Equations, Exercise 4: EXERCISE

Attempt the free practice questions on Chapter 4: Quadratic Equations, Exercise 4: EXERCISE with hints and solutions to strengthen your understanding. Modern's abc+ of Mathematics for Class 10 solutions are prepared by Experienced Embibe Experts.