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Asked by sudhanshubhushanroy 25th November 2017, 4:04 PM
Answered by Expert
Answer:
begin mathsize 16px style straight alpha space and space straight beta space are space the space roots space of space the space equation space ax squared plus bx plus straight c equals 0
rightwards double arrow straight alpha plus straight beta equals fraction numerator negative straight b over denominator straight a end fraction space and space αβ equals straight c over straight a
for space the space second space given space equation space also
straight alpha to the power of 4 plus straight beta to the power of 4 equals fraction numerator negative straight m over denominator straight l end fraction
straight alpha to the power of 4 straight beta to the power of 4 equals straight n over straight l
Let space straight x subscript 1 comma straight x subscript 2 space be space the space roots space of space the space straight a squared lx squared minus 4 aclx plus 2 straight c squared straight l plus straight a squared straight m equals 0
straight x subscript 1 plus straight x subscript 2 equals fraction numerator 4 acl over denominator straight a squared straight l end fraction equals fraction numerator 4 straight c over denominator straight a end fraction equals 4 αβ
straight x subscript 1 straight x subscript 2 equals fraction numerator 2 straight c squared straight l plus straight a squared straight m over denominator straight a squared straight l end fraction equals negative open parentheses straight alpha minus straight beta close parentheses squared
Product space is space negative space hence space roots space are space opposite space in space sign. end style
Answered by Expert 25th November 2017, 7:12 PM
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