The equation formed by multiplying each root of `ax^(2) + bx+ c = 0" by "2 " is "x^(2) = 36x + 24 =0`
If `alpha and beta` are the roots of the equation `x^(2) + x+ 2 = 0`, then what is `(alpha ^(10) + beta^(10))/(alpha^(-10)+beta^(-10))` equal to ?

Options

A. 4096
B. 2048
C. 1024
D. 512

Answer

C

Explanation

Here , `alpha and beta` are the roots of the equation
`x^(2) + x + 2 = 0 `
`alpha+ beta = -1`
`alpha beta = 2`
` (alpha^(10) + beta^(10))/(alpha^(-10) + beta^(-10))= (alpha^(10)+beta^(10))/(1/alpha^(10) + 1/beta^(10 ))`
` ((alpha^(10) + beta^(10))(alpha beta)^(10))/((alpha^(10)+beta^(10)) )=(alpha beta)^(10)`
` :. (alpha beta)^(10)=2^(10=1024`