Question 3 - Miscellaneous - Chapter 4 Class 12 Determinants
Last updated at Dec. 16, 2024 by Teachoo
Miscellaneous
Misc 2
Misc 3 Important
Misc 4
Misc 5
Misc 6
Misc 7 Important
Misc 8 (MCQ)
Misc 9 (MCQ) Important
Matrices and Determinants - Formula Sheet and Summary Important
Question 1 Important
Question 2
Question 3 You are here
Question 4 Important
Question 5 Important
Question 6 Important
Question 7
Question 8
Question 9 Important
Question 10 (MCQ) Important
Last updated at Dec. 16, 2024 by Teachoo
Question 3 Solve the equations 𝑥+𝑎𝑥𝑥𝑥𝑥+𝑎𝑥𝑥𝑥𝑥+𝑎 = 0, a ≠ 0 Solving ∆ = 𝑥+𝑎𝑥𝑥𝑥𝑥+𝑎𝑥𝑥𝑥𝑥+𝑎 Applying R1 → R1 + R2 + R3 = 𝑥+𝑎+𝑥+𝑥𝑥+𝑥+𝑎+𝑥𝑥+𝑥+𝑥+𝑎𝑥𝑥+𝑎𝑥𝑥𝑥𝑥+𝑎 = 𝟑𝒙+𝒂𝟑𝒙+𝒂𝟑𝒙+𝒂𝑥𝑥+𝑎𝑥𝑥𝑥𝑥+𝑎 Taking (3x + a) common from R1 = (3x + a) 111𝑥𝑥+𝑎𝑥𝑥𝑥𝑥+𝑎 Applying C2 → C2 – C1 = (3x + a) 1𝟏−𝟏1𝑥𝑥+𝑎−𝑥𝑥𝑥𝑥−𝑥𝑥+𝑎 = (3x+ a) 1𝟎1𝑥𝑎𝑥𝑥0𝑥+𝑎 Applying C3 →C3 – C1 = (3x + a) 10𝟏−𝟏𝑥𝑎𝑥−𝑥𝑥0𝑥+𝑎−𝑥 = (3x + a) 10𝟎𝑥𝑎0𝑥0𝑎 = (3x+ a) 1 𝑎00𝑎−0 𝑥0𝑥0+0 𝑥𝑎𝑥0 = (3x+ a) 1 𝑎00𝑎−0+0 = (3x+ a) (1(a2 – 0) – 0 + 0) = (3x+ a) (a2) ∴ ∆ = (3x+ a) (a2) Given ∆ = 0 ∴ (3x + a) a2 = 0