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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`

A

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

B

` x^2 + 12 x + 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)^(101)))/(1-omega)=1`
`b=1+omega^(6)+omega^(12)+......+omega^(60)=11, " "x^(2)-12x+11=0`
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