Let λ≠0 be in R. If α and β are the roots of the equation, x^2-x+2λ=0 and α and γ are the roots of the equation, 3x^2-10x+27λ=0, then (βγ)/(λ) is…

Question

Let λ≠0 be in R. If α and β are the roots of the equation, x^2-x+2λ=0 and α and γ are the roots of the equation, 3x^2-10x+27λ=0, then (βγ)/(λ) is equal to:

MARKS Content Team · Accepted Answer

Correct answer: (B) 18. Satisfying α we have, 3α^2-10α+27λ=0 …i and 3α^2-3α+6λ=0 …ii Subtract -7α+21λ=0 3λ=α by ii, 9λ^2-3λ+2λ=0 ⇒λ=0,1/9 but λ≠0 ∴ Given equation are x^2-x+2/9=0 and 3x^2-10x+3=0 ∴α=1/3,β=2/3,α=1/3,γ=3 ∴(βγ)/(λ)=(23·3)/19=18

Let $λ \neq 0$ be in $R$ . If $α$ and $β$ are the roots of the equation, $x^{2} - x + 2 λ = 0$ and $α$ and $γ$ are the roots of the equation, $3 x^{2} - 10 x + 27 λ = 0,$ then $\frac{β γ}{λ}$ is equal to:

Solution

Relevant Questions

Let λ≠0 be in R. If α and β are the roots of the equation, x2-x+2λ=0 and α and γ are the roots of the equation, 3x2-10x+27λ=0, then βγλ is equal to:

Solution

Relevant Questions

Let $λ \neq 0$ be in $R$ . If $α$ and $β$ are the roots of the equation, $x^{2} - x + 2 λ = 0$ and $α$ and $γ$ are the roots of the equation, $3 x^{2} - 10 x + 27 λ = 0,$ then $\frac{β γ}{λ}$ is equal to: