If a and b are the zeros of polynomial f(x)=x^2 -1 then find the equations whose zeros are 2a/b and 2b/a.

Asked by Rashee Soni | 11th May, 2014, 12:00: PM

Expert Answer:

C o n s i d e r comma space  x squared minus 1 equals 0  a plus b equals 0 space a n d space a b space equals minus 1 space space space... space left parenthesis i right parenthesis  T h e space e q u a t i o n space w h o s e space r o o t s space a r e space fraction numerator 2 a over denominator b end fraction space a n d space fraction numerator 2 b over denominator a end fraction space i s space g i v e n space b y  x squared minus open parentheses fraction numerator 2 a over denominator b end fraction plus fraction numerator 2 b over denominator a end fraction close parentheses x plus fraction numerator 2 a over denominator b end fraction fraction numerator 2 b over denominator a end fraction equals 0  rightwards double arrow x squared minus 2 open parentheses fraction numerator a squared plus b squared over denominator a b end fraction close parentheses x plus 4 equals 0  rightwards double arrow x squared minus 2 open square brackets fraction numerator open parentheses a plus b close parentheses squared minus 2 a b over denominator a b end fraction close square brackets x plus 4 equals 0 F r o m space left parenthesis i right parenthesis comma space w e space g e t  x squared minus 2 open square brackets fraction numerator 0 minus 2 cross times minus 1 over denominator minus 1 end fraction close square brackets x plus 4 equals 0  rightwards double arrow x squared plus 4 x plus 4 equals 0

Answered by Avinash Soni | 11th May, 2014, 12:14: PM