UPSC NDA Math Model Paper 7

Given equation are 2x2+3x+5λ=0 and x2+2x+3λ=0
To Find: Value of λ
2x2+3x+5λ=0 .... (1)
x2+2x+3λ=0 .... (2)
Subtracting [2 × equation (2) - equation (1)], we get
⇒2x2+4x+6λ−(2x2+3x+5λ) =0−0
⇒ x + λ = 0
∴ x = -λ
Put the value of x in equation (1), we get
⇒2(−λ)2+3(−λ)+5λ=0
⇒2λ2+2λ=0
⇒ 2λ (λ + 1) = 0
∴ λ = 0 and -1