if alpha and beta are the zeroes of quadratic polynomial f(x)= ax2+bx+c, then evaluate alpha4+beta4

Asked by manavmansvi | 21st Jun, 2015, 04:48: PM

Expert Answer:

$alpha space a n d space beta space a r e space r o o t s space o f space a x squared plus b x plus c equals 0 rightwards double arrow alpha plus beta equals negative b over a alpha beta equals c over a alpha squared plus beta squared equals open parentheses alpha plus beta close parentheses squared minus 2 alpha beta equals b squared over a squared minus 2 c over a equals fraction numerator b squared minus 2 a c over denominator a squared end fraction alpha to the power of 4 plus beta to the power of 4 equals open parentheses alpha squared plus beta squared close parentheses squared minus 2 alpha squared beta squared equals open parentheses fraction numerator b squared minus 2 a c over denominator a squared end fraction close parentheses squared minus 2 open parentheses c over a close parentheses squared equals fraction numerator b to the power of 4 plus 4 a squared c squared minus 4 a b squared c minus 2 a squared c squared over denominator a to the power of 4 end fraction equals fraction numerator b to the power of 4 plus 2 a squared c squared minus 4 a b squared c over denominator a to the power of 4 end fraction$

Answered by satyajit samal | 22nd Jun, 2015, 01:10: AM

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