alpha comma beta & space gamma space a r e space t h e space z e r o s space o f space p o l y n o m i a l space  6 x cubed plus 5 x squared minus 5 x plus 1,then space find space the space value space of1 over alpha plus 1 over beta plus 1 over gamma

Asked by mahika784 | 21st Jun, 2014, 12:00: PM

Expert Answer:

C o n s i d e r space t h e space g i v e n space p o l y n o m i a l comma space 6 x cubed plus 5 x squared minus 5 x plus 1 C o n s i d e r space t h e space g i v e n space e x p r e s s i o n space 1 over alpha plus 1 over beta plus 1 over gamma : 1 over alpha plus 1 over beta plus 1 over gamma equals fraction numerator beta gamma plus alpha gamma plus alpha beta over denominator alpha beta gamma end fraction W e space k n o w space t h a t space beta gamma plus alpha gamma plus alpha beta equals c over a comma space a n d space alpha beta gamma equals space fraction numerator minus d over denominator a end fraction space f o r space a space p o l y n o m i a l comma space a x cubed plus b x squared plus c x plus d equals 0 space rightwards double arrow beta gamma plus alpha gamma plus alpha beta equals fraction numerator minus 5 over denominator 6 end fraction space a n d space alpha beta gamma equals space fraction numerator minus 1 over denominator 6 end fraction rightwards double arrow fraction numerator beta gamma plus alpha gamma plus alpha beta over denominator alpha beta gamma end fraction equals fraction numerator fraction numerator minus 5 over denominator 6 end fraction over denominator fraction numerator minus 1 over denominator 6 end fraction end fraction equals 5 rightwards double arrow fraction numerator beta gamma plus alpha gamma plus alpha beta over denominator alpha beta gamma end fraction equals 5

Answered by Vimala Ramamurthy | 21st Jun, 2014, 12:50: PM