FINS THE VALUE OF K IF ONE ROOT OF THE QUADRATIC EQUATION KX^2-14X+8 IS 6 TIMES THE OTHER.

Asked by dalbirgolagarh | 19th Jan, 2016, 04:32: PM

Expert Answer:

begin mathsize 14px style G i v e n space e q u a t i o n space i s space K X squared minus 14 X plus 8 equals 0 H e r e comma space a equals K comma space b equals negative 14 space a n d space c equals 8 L e t space alpha space a n d space beta space b e space t h e space r o o t s space o f space t h e space g i v e n space e q u a t i o n. T h e n comma space alpha equals 6 beta N o w comma space alpha plus beta equals negative b over a equals negative fraction numerator left parenthesis negative 14 right parenthesis over denominator K end fraction equals 14 over K rightwards double arrow 6 beta plus beta equals 14 over K rightwards double arrow 7 beta equals 14 over K rightwards double arrow beta equals 2 over K alpha beta equals c over a equals 8 over K rightwards double arrow left parenthesis 6 beta right parenthesis beta equals 8 over K rightwards double arrow 6 beta squared equals 8 over K rightwards double arrow 3 beta squared equals 4 over K rightwards double arrow 3 open parentheses 2 over K close parentheses squared equals 4 over K rightwards double arrow 3 cross times 4 over K squared equals 4 over K rightwards double arrow fraction numerator 3 cross times 4 over denominator 4 end fraction equals K squared over K rightwards double arrow 3 equals K rightwards double arrow K equals 3 end style

Answered by Rashmi Khot | 19th Jan, 2016, 05:37: PM

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