If alpha and beta are tge zeros of quadratic polynomial f(x)= ax^2 + bx+c ,then evaluate alpha to the power of 4+beta to the power of 4.

Asked by jatin452002 | 7th Jun, 2017, 07:03: PM

Expert Answer:

begin mathsize 16px style Since space straight alpha space and space straight beta space are space the space zeros space of space the space quadratic space polynomial space ax squared plus bx plus straight c comma space we space have
straight alpha plus straight beta equals negative straight b over straight a space and space αβ equals straight c over straight a
Now comma
straight alpha to the power of 4 plus straight beta to the power of 4 equals open parentheses straight alpha squared plus straight beta squared close parentheses squared minus 2 straight alpha squared straight beta squared
rightwards double arrow straight alpha to the power of 4 plus straight beta to the power of 4 equals open square brackets open parentheses straight alpha plus straight beta close parentheses squared minus 2 αβ close square brackets squared minus 2 left parenthesis αβ right parenthesis squared
rightwards double arrow straight alpha to the power of 4 plus straight beta to the power of 4 equals open square brackets open parentheses negative straight b over straight a close parentheses squared minus 2 cross times straight c over straight a close square brackets squared minus 2 open parentheses straight c over straight a close parentheses squared
rightwards double arrow straight alpha to the power of 4 plus straight beta to the power of 4 equals open square brackets fraction numerator straight b squared minus 2 ac over denominator straight a squared end fraction close square brackets squared minus fraction numerator 2 straight c squared over denominator straight a squared end fraction
rightwards double arrow straight alpha to the power of 4 plus straight beta to the power of 4 equals fraction numerator open parentheses straight b squared minus 2 ac close parentheses squared minus 2 straight a squared straight c squared over denominator straight a to the power of 4 end fraction end style

Answered by Rashmi Khot | 8th Jun, 2017, 09:07: AM