Algebra and Applications Test 2

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Question : 30 of 40

Marks: +1, -0

If

δ

and

σ

are the roots of

v ^2 + k = 0

, where k is a prime, then which equation has the roots

1/δ

and

1/σ

?

$1/v^2+1/k=0$
$kv^2+1=0$
$kv^2-1=0$
$1/v^2-1/k=0$
None of these

Solution:

Since

δ

and

σ

are roots of

v^2 + k = 0

,
Then

δ+σ=0

And

\ασ = k

∴1/δ+1/σ={δ+σ}/{δσ}=0

and

1/{δσ}=1/k

∴ Equation is

v^2-(1/δ+1/σ)v+1/{δσ}=0

⇒v^2-0v+1/{k}=0

⇒kv^2+1=0

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