NIMCET 2008 Question Paper with solutions

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Question : 10 of 120

Marks: +1, -0

Let

α

and

β

be the roots of the equation

x^{2}+x+1=0

The equation whose roots are

α^{19}

and

β^{7}

is

$x^{2}-x-1=0$
$x^{2}+x-1=0$
$x^{i}-x+1=0$
$x^{2}+x+1=0$

Solution:

α, β

are roots of

x^{2}+x+1=0

α+β=-1, α β=1

⇒ α=w ; β=w^{2}

⇒ α^{19}=α ; β^{7}=w^{2}=β

α^{19}+β^{7}=α+β=-1

α^{19} ⋅ β^{7}=α β=1

Hence, the equation remans same.

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