Algebra and Applications Test 1

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Question : 14 of 40

Marks: +1, -0

If the roots of the equation

q^2 + q + 1 = 0

are in the ratio of j : k, then which one of the following relations holds true?

$j + k + 1 = 0$
$j/k+k/j+1=0$
$√j+√k+1=0$
$√{j/k+√{k/j+1}}=0$
None of these

Solution:

Let the roots of

q^2 + q + 1 = 0

are jσ and kσ

∴jσ+kσ=-1

⇒σ=-1/{j+k}

and

jσ.kσ=1

⇒jk(-1/{j+k})^2=1

⇒jk=(j+k)^2

⇒jk=j^2+k^2+2jk

⇒1=j/k+k/j+2

⇒j/k+k/j+1=0

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