1. Class 10
  2. Solutions of Sample Papers for Class 10 Boards
  3. CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard
Check sibling questions

Question 30 - CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at Dec. 16, 2024 by Teachoo

Obtain all the zeros of the polynomial x 4 + 4x 3 − 2x 2 − 20x − 15, if two of its zeroes are √5 and −√5.

 

Note : This is similar to Example 9 of NCERT – Chapter 2 Class 10

Check the answer here https://www.teachoo.com/1503/496/Example-9---Find-all-zeroes-of-2x4---3x3---3x2---6x---2/category/Examples/

Transcript

Question 30 Obtain all the zeros of the polynomial x4 + 4x3 − 2x2 − 20x − 15, if two of its zeroes are √5 and −√5. Let p(x) = x4 + 4x3 − 2x2 − 20x − 15 Since x = √5 is a zero , x – √5 is a factor Since x = – √5 is a zero , x + √5 is a factor Hence , (x + √5) (x – √5) is a factor i.e. (x2 – (√5)^2) is also a factor i.e. (x2 – 5) is also a factor Now, by dividing the given polynomial by (x2 – 5) We can find out other factors Now, we factorize x2 + 4x + 3 x2 + 4x + 3 We use splitting the middle term method = x2 + 3x + x + 3 = x(x + 3) + 1(x + 3) = (x + 1)(x + 3) Splitting the middle term method We need to find two numbers whose Sum = 4 Product = 3 × 1 = 3 ∴ x = –1 & x = –3 are the zeroes of p(x) Therefore, the zeroes of p(x) are √5, –√5, –1, and –3
  1. Class 10
  2. Solutions of Sample Papers for Class 10 Boards

    3. CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard

    CBSE Class 10 Sample Paper for 2020 Boards - Maths Basic →
CBSE Class 10 Sample Paper for 2020 Boards - Maths Basic →
Class 10
Solutions of Sample Papers for Class 10 Boards

About the Author

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo