Misc 5 - Solve |x+a x x x x+a x x x x+a| = 0 - Class 12 - Miscellaneous

Misc 5 - Chapter 4 Class 12 Determinants - Part 2
Misc 5 - Chapter 4 Class 12 Determinants - Part 3

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Transcript

Question 3 Solve the equations 𝑥+𝑎﷮𝑥﷮𝑥﷮𝑥﷮𝑥+𝑎﷮𝑥﷮𝑥﷮𝑥﷮𝑥+𝑎﷯﷯ = 0, a ≠ 0 Solving ∆ = 𝑥+𝑎﷮𝑥﷮𝑥﷮𝑥﷮𝑥+𝑎﷮𝑥﷮𝑥﷮𝑥﷮𝑥+𝑎﷯﷯ Applying R1 → R1 + R2 + R3 = 𝑥+𝑎+𝑥+𝑥﷮𝑥+𝑥+𝑎+𝑥﷮𝑥+𝑥+𝑥+𝑎﷮𝑥﷮𝑥+𝑎﷮𝑥﷮𝑥﷮𝑥﷮𝑥+𝑎﷯﷯ = 𝟑𝒙+𝒂﷮𝟑𝒙+𝒂﷮𝟑𝒙+𝒂﷮𝑥﷮𝑥+𝑎﷮𝑥﷮𝑥﷮𝑥﷮𝑥+𝑎﷯﷯ Taking (3x + a) common from R1 = (3x + a) 1﷮1﷮1﷮𝑥﷮𝑥+𝑎﷮𝑥﷮𝑥﷮𝑥﷮𝑥+𝑎﷯﷯ Applying C2 → C2 – C1 = (3x + a) 1﷮𝟏−𝟏﷮1﷮𝑥﷮𝑥+𝑎−𝑥﷮𝑥﷮𝑥﷮𝑥−𝑥﷮𝑥+𝑎﷯﷯ = (3x+ a) 1﷮𝟎﷮1﷮𝑥﷮𝑎﷮𝑥﷮𝑥﷮0﷮𝑥+𝑎﷯﷯ Applying C3 →C3 – C1 = (3x + a) 1﷮0﷮𝟏−𝟏﷮𝑥﷮𝑎﷮𝑥−𝑥﷮𝑥﷮0﷮𝑥+𝑎−𝑥﷯﷯ = (3x + a) 1﷮0﷮𝟎﷮𝑥﷮𝑎﷮0﷮𝑥﷮0﷮𝑎﷯﷯ = (3x+ a) 1 𝑎﷮0﷮0﷮𝑎﷯﷯−0 𝑥﷮0﷮𝑥﷮0﷯﷯+0 𝑥﷮𝑎﷮𝑥﷮0﷯﷯﷯ = (3x+ a) 1 𝑎﷮0﷮0﷮𝑎﷯﷯−0+0﷯ = (3x+ a) (1(a2 – 0) – 0 + 0) = (3x+ a) (a2) ∴ ∆ = (3x+ a) (a2) Given ∆ = 0 ∴ (3x + a) a2 = 0

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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.