Find the quadratic polynomial, sum of whose zeroes is 5 2 and their product is 1 . Hence, find the zeroes of the polynomial.

Let α and β be the zeroes of the required polynomial f ( x ) . Then ( α + β ) = 5 2 and α β = 1 ∴ f ( x ) = x 2 - ( ∝ + β ) x + ∝ β ⇒ f ( x ) = x 2 - 5 2 x + 1 Hence, the required polynomial is f ( x ) = x 2 - 5 2 x + 1 To find the zeroes of the polynomial, f ( x ) = 0 ∴ x 2 - 5 2 x + 1 = 0 ⇒ 2 x 2 - 5 x + 2 = 0 ⇒ 2 x 2 – ( 4 x + x ) + 2 = 0 ⇒ 2 x 2 – 4 x – x + 2 = 0 ⇒ 2 x ( x – 2 ) – 1 ( x – 2 ) = 0 ⇒ ( 2 x – 1 ) ( x – 2 ) = 0 ⇒ ( 2 x – 1 ) = 0 o r ( x – 2 ) = 0 ⇒ x = 1 2 or x = 2 So, the zeros of f ( x ) are 1 2 and 2

Find the quadratic polynomial, sum of whose roots is 2 and their product is 1 3 .

We can find the quadratic equation if we know the sum of the roots and product of the roots. By using the formula f ( x ) = x 2 - ( α + β ) x + α β , where α , β are the roots of the quadratic polynomial. Given : Sum of the roots α + β = 2 and product of the roots α β = 1 3 ∴ f ( x ) = x 2 - 2 x + 1 3 Hence the quadratic polynomial is x 2 - 2 x + 1 3 .

E M B I B E

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

R S Aggarwal and Veena Aggarwal Solutions for Exercise 1: Exercise 2A

Author:R S Aggarwal & Veena Aggarwal

R S Aggarwal Mathematics Solutions for Exercise - R S Aggarwal and Veena Aggarwal Solutions for Exercise 1: Exercise 2A

Attempt the free practice questions from Exercise 1: Exercise 2A with hints and solutions to strengthen your understanding. Secondary School Mathematics for Class 10 solutions are prepared by Experienced Embibe Experts.

Questions from R S Aggarwal and Veena Aggarwal Solutions for Exercise 1: Exercise 2A with Hints & Solutions

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 2 - Polynomials>Exercise 2A>Q 2

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients $x^{2} - 2 x - 8$

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 2 - Polynomials>Exercise 2A>Q 5

Find the zeroes of the quadratic polynomial $f (x) = 5 x^{2} - 4 - 8 x$ and verify the relationship between the zeroes and coefficients of the given polynomial.