[" Let "alpha=(-1+i sqrt(3))/(2)" .If "a=(1+alpha)sum_(k=0)^(100)alpha^(2k)" and "b=sum_(k=0)^(100)alpha^(3k)" ,then a and "b" are the roots of the quadratic equation: "],[[" (1) "x^(2)-102x+101=0," (2) "x^(2)+101x+100=0],[" (3) "x^(2)-101x+100=0," (4) "x^(2)+102x+101=0]]

Let alpha=(-1+isqrt(3))/2 and a=(1+alpha)sum_(k=0)^(100) alpha^(2k),b=sum_(k=0)^(100) alpha^(3k) . If a and b are roots of quadratic equation then quadratic equation is

Let alpha=(-1+isqrt(3))/2 and a=(1+alpha)sum_(k=0)^(100) alpha^(2k),b=sum_(k=0)^(100) alpha^(3k) . If a and b are roots of quadratic equation then quadratic equation is

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 :

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

If alpha & beta are the roots of the quadratic equation x^(2)-(k-2)x-k+1=0 ,then minimum value of alpha^(2)+beta^(2) is

If alpha & beta are the roots of the quadratic equation x^(2)-(k-2)x-k+1=0 , then minimum value of alpha^(2)+beta^(2) is

If alpha=e^(2 pi(i)/(11)) and f(x)=5+sum_(k=1)^(60)A_(x)^(k), then the value of sum_(r=0)^(10)f(alpha^(r)x) is

If alpha and beta are the real roots of the equation x^(2)-(k+1)x-(k+2)=0, then minimum value of alpha^(2)+beta^(2) is