Question
Question: If a non-zero root of the equation x<sup>2</sup> + 2x + 3λ = 0 and 2x<sup>2</sup> + 3x + 5λ = 0 is ...
If a non-zero root of the equation x2 + 2x + 3λ = 0 and
2x2 + 3x + 5λ = 0 is common, then the value of λ will be-
A
2
B
1
C
–1
D
0
Answer
–1
Explanation
Solution
Let α be the common root.
α2 + 2α + 3λ = 0 … (i)
and 2α2 + 3α + 5λ = 0 ….(ii)
By (i) and (ii), α = – λ
In equation (i), λ2 –2λ + 3λ = 0
= 0, –1, λ = –1 (Q λ ≠ 0 ⇒ α ≠ 0)