Question

Solution for this question pls.....
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Answer 1

Answer:

(C) 254

Step-by-step explanation:

From the first quadratic:

λx² - ( λ - 1 )x + 5 = λ ( x - α ) ( x - β )

we have    λ ( α + β ) = λ - 1    and    λαβ = 5.

Now...

α/β + β/α = 4/5

=> 5 ( α² + β² ) = 4αβ

=> 5λ ( α² + β² ) = 4λαβ = 4×5

=> λ ( α² + β² ) = 4

=> λ ( ( α + β )² - 2αβ ) = 4

=> ( λ ( α + β ) )²  -  2αβλ² = 4λ

=> ( λ - 1 )² - 10λ = 4λ

=> λ² - 16λ + 1 = 0

=> λ₁ + λ₂ = 16  and  λ₁λ₂ = 1

=> λ₁² + λ₂²  =  ( λ₁ + λ₂ )² - 2λ₁λ₂  =  16² - 2 = 254

=> λ₁/λ₂ + λ₂/λ₁ = ( λ₁² + λ₂² ) / ( λ₁λ₂ ) = 254 / 1 = 254