If , are the roots of x^2-x+1=0, then the quadratic equation whose roots are ^2015 , ^2015 is

Question

Accepted Answer

Correct answer: A. (b) We have, x^2-x+1=0 x= , ^2 So, = and = ^2 Now, ^2015= ^2015= ^2013 ^2= ^3 671 ^2= ^2 ( ∵ ^3=1) ^2015= ( ^2 )^2015= ^4030= ^4029 = ^3 1343= ∴ ^2015+ ^2015= ^2+ =-1( ∵ ^2+ +1=0) and ^2015 ^2015= ^2 = ^3=1 ∴ Equation whose roots are ^2015 and ^2015 will be x^2-(-1)x+1=0 x^2+x+1=0

$If α, β are the roots of x^{2} - x + 1 = 0, then the quadratic equation whose roots are α^{2015}, β^{2015} is$

Solution

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