Ex 2.3

Chapter 2 Class 10 Polynomials
Serial order wise

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### Transcript

Ex2.3, 3 Obtain all other zeroes of 3x4 + 6x3 – 2x2 – 10x - 5 , if two of its zeroes are √(5/3) and -√(5/3) . Introduction 2 is a factor of 6 3 is a factor of 6 So, 2 × 3 is also a factor of 6 We will use the same in our question Ex2.3, 3 Obtain all other zeroes of 3x4 + 6x3 – 2x2 – 10x - 5 , if two of its zeroes are √(5/3) and -√(5/3) . Let p(x) = 3x4 + 6x3 – 2x2 – 10x - 5 Since x =√(5/3) is a zero , x – √(5/3) is a factor & x = –√(5/3) is a zero , x + √(5/3) is a factor Hence ("x +" √(5/3)) ("x –" √(5/3)) is also a factor = (x2 – (√(5/3))^2) = (x2 – 5/3) Now by dividing the given polynomial by (x2 – 5/3) We can find out other factors Now, we factorize 3x2 + 6x + 3 3x2 + 6x + 3 We find roots using splitting the middle term method = 3x2 + 3x + 3x + 3 = 3x(x + 1) +3 (x + 1) = (3x + 3)(x + 1) = 3(x + 1)(x + 1) = 3(x + 1)(x + 1) = 3(x + 1)2 Hence, x + 1 = 0 i.e. x = – 1 , – 1 is a zero of p(x) Therefore, the zeroes of p(x) are√(5/3), -√(5/3), −1 and – 1.

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#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.