If x + 1 x x x x + λ x x x x + λ 2 = 9 8 103 x + 81 , then λ , λ 3 are the roots of the equation

Step-by-step solution

Given that, x + 1 x x x x + λ x x x x + λ 2 = 9 8 103 x + 81 Put x = 0 as x ∈ R ⇒ 1 0 0 0 λ 0 0 0 λ 2 = 9 8 103 0 + 81 On expanding the determinant we get, ⇒ λ 3 = 9 8 × 81 ⇒ λ 3 = 9 3 2 3 ⇒ λ = 9 2 and λ 3 = 9 6 Now the required quadratic equation is x 2 - 9 2 + 9 6 x + 9 2 × 9 6 = 0 ⇒ x 2 - 6 x + 27 4 = 0 ⇒ 4 x 2 - 24 x + 27 = 0 Hence, the required quadratic equation is 4 x 2 - 24 x + 27 = 0