Last updated at May 29, 2018 by Teachoo

Transcript

Ex 4.3 ,3 Find the roots of the following equations: (i) x โ 1/๐ฅ=3,๐ฅโ 0 x โ 1/๐ฅ=3 (๐ฅ(๐ฅ) โ 1 )/๐ฅ = 3 (๐ฅ^2 โ 1 )/๐ฅ = 3 x2 โ 1 = 3x x2 โ 3x โ 1 = 0 Comparing equation with ax2 + bx + c = 0 So, a = 1, b = โ3, c = โ1 We know that D = b2 โ 4ac D = ( โ3)2 โ 4ร1รโ1 D = 9 + 4 D = 13 Hence, roots to equation are given by x = (โ ๐ ยฑ โ๐ท)/2๐ Putting values x = (โ (โ 3) ยฑ โ13)/(2 ร 1) x = (3 ยฑ โ13)/2 Hence, roots to equation are x = (3 + โ13)/2 or x = (3 โ โ13)/2 Ex 4.3 ,3 Find the roots of the following equations: (ii) 1/(๐ฅ + 4)โ1/(๐ฅ โ 7)=11/30,๐ฅโ โ4, 7 1/(๐ฅ + 4)โ1/(๐ฅ โ 7)=11/30 ((๐ฅ โ 7) โ (๐ฅ + 4))/((๐ฅ + 4)(๐ฅ โ 7)) = 11/30 (๐ฅ โ 7 โ ๐ฅ โ 4)/((๐ฅ + 4)(๐ฅ โ 7)) = 11/30 (โ11)/((๐ฅ + 4)(๐ฅ โ 7))=11/30 โ(11 ร 30)/11=(๐ฅ+4)(๐ฅโ7) โ30 = (x + 4) (x โ 7) (x + 4) (x โ 7) = โ30 x (x โ 7) + 4 (x โ 7) = โ30 x2 โ 7x + 4x โ 28 = โ30 x2 โ 3x โ 28 = โ30 x2 โ 3x โ 28 + 30 = 0 x2 โ 3x + 2 = 0 Factorizing by quadratic method Comparing with ax2 + bx + c = 0 Here a = 1, b = โ 3, c = 2 We know that D = b2 โ 4ac D = ( โ 3)2 โ 4ร1ร2 D = 9 โ 8 D = 1 Hence roots to equation are x = (โ ๐ ยฑ โ๐ท)/2๐ Putting the values x = (โ (โ 3) ยฑ โ1)/(2 ร 1) x =(3 ยฑ 1)/2 Solving Hence x = 2 and x = 1 are the roots of the equation

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.