If a and b are the zeroes of the polynomial f(x)=2x^2+11x+5 then find
a^4+b^4   and    1/a+1/b-2ab

Asked by vans75a | 14th Aug, 2015, 09:53: PM

Expert Answer:

I f space a space a n d space b space a r e space t h e space z e r o e s space o f space t h e space p o l y n o m i a l space f left parenthesis x right parenthesis equals 2 x squared plus 11 x plus 5 comma space t h e n a plus b equals negative 11 over 2 a b equals 5 over 2 left parenthesis i right parenthesis space a to the power of 4 plus b to the power of 4 equals open parentheses a squared plus b squared close parentheses squared minus 2 a squared b squared equals open parentheses open parentheses a plus b close parentheses squared minus 2 a b close parentheses squared minus 2 open parentheses a b close parentheses squared equals open parentheses open parentheses negative 11 over 2 close parentheses squared minus 2 cross times 5 over 2 close parentheses squared minus 2 open parentheses 5 over 2 close parentheses squared equals open parentheses 121 over 4 minus 5 close parentheses squared minus 25 over 2 equals open parentheses 101 over 4 close parentheses squared minus 25 over 2 equals 10201 over 16 minus 25 over 2 equals fraction numerator 10201 minus 200 over denominator 16 end fraction equals 10001 over 16 left parenthesis i i right parenthesis space 1 over a plus 1 over b minus 2 a b equals fraction numerator a plus b over denominator a b end fraction minus 2 a b equals fraction numerator negative 11 divided by 2 over denominator 5 divided by 2 end fraction minus 2 open parentheses 5 over 2 close parentheses equals negative 11 over 5 minus 5 equals negative fraction numerator 11 plus 25 over denominator 5 end fraction equals negative 36 over 5

Answered by satyajit samal | 15th Aug, 2015, 07:02: AM