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Let alpha=(-1+isqrt3)/2. If a =(1 +alpha...

Let `alpha=(-1+isqrt3)/2`. If `a =(1 +alpha^2)underset(k-0)overset(100)(Sigma)alpha^k` and `b = underset(k-0)overset(10)(Sigma)alpha^(6k)`, , then a and b are the roots of the quadratic equation :

A

`x^2 - 102x + 11 =0`

B

`x^2 + 12x + 11 =0`

C

`x^2 - 12 x - 11 =0`

D

`x^2 - 12 x+ 11=0`

Text Solution

Verified by Experts

The correct Answer is:
D
`alpha = omega ," "a = (1+omega^2) (1 + omega + omega^2 +...+ omega ^(100))`
`a = (1+omega^2)((1-(omega)^(100)))/(1-omega)=1`
` b=1 +omega^6 +omega^(12)+...+omega ^(60)=11," "x^2 -12 + 11=0`
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