Write the zeros of the quadratic polynomial f ( x ) = 4 3 x 2 + 5 x – 2 3 .

Let f x be the given polynomial. f ( x ) = 4 3 x 2 + 5 x - 2 3 To find the zeros of the quadratic polynomial we will equate f ( x ) to 0 . ∴ f ( x ) = 0 ⇒ 4 3 x 2 + 5 x – 2 3 = 0 ⇒ 4 3 x 2 + 8 x - 3 x - 2 3 = 0 ⇒ 4 x ( 3 x + 2 ) - 3 ( 3 x + 2 ) = 0 ⇒ ( 4 x - 3 ) ( 3 x + 2 ) = 0 x = 3 4 , - 2 3 Hence, zeros of the quadratic polynomial are 3 4 , - 2 3

If α , β are the zeroes of the polynomial f ( x ) = x 2 + x – 2 , then 1 α - 1 β

By using the relationship between the zeroes of the quadratic polynomial. We have Sum of zeroes = - ( Coefficient of x ) ( Coefficient of x 2 ) and Product of zeroes = ( Constant term ) ( Coefficient of x 2 ) ∴ α + β = - 1 1 and α β = - 2 1 ⇒ α + β = - 1 and α β = - 2 Now, 1 α - 1 β 2 = ( β - α ) ( α β ) 2 = ( α + β ) 2 - 4 α β ( α β ) 2 ∵ ( β - α ) 2 = ( α + β ) 2 - 4 α β = ( - 1 ) 2 - 4 ( - 2 ) ( - 2 ) 2 [ ∵ α + β = - 1 and α β = - 2 ] = 9 4 ∵ 1 α - 1 β 2 = 9 4 ⇒ 1 α - 1 β = ± 3 2 “Note: Answer mentioned in the book is incorrect the correct answer is: ± 3 2 ”

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Secondary School Mathematics for Class 10>Algebra>Chapter 2 - Polynomials>Exercise 2C

R S Aggarwal and Veena Aggarwal Solutions for Exercise 4: Exercise 2C

Author:R S Aggarwal & Veena Aggarwal

R S Aggarwal Mathematics Solutions for Exercise - R S Aggarwal and Veena Aggarwal Solutions for Exercise 4: Exercise 2C

Attempt the free practice questions from Exercise 4: Exercise 2C with hints and solutions to strengthen your understanding. Secondary School Mathematics for Class 10 solutions are prepared by Experienced Embibe Experts.