sir
   if alpha ,beeta ,gamma are zeroes of polynomials f(x)=2x^3+6x^2-4x+9,find the value of 1/alphabeeta+1/beetagammma+1/gamma alpha

Asked by seeni2005 | 19th Jul, 2016, 06:30: PM

Expert Answer:

begin mathsize 16px style Given space that space straight alpha comma space straight beta comma space straight gamma space are space the space zeroes space of space the space polynomial space straight f left parenthesis straight x right parenthesis space equals 2 straight x cubed plus space 6 straight x squared space minus 4 straight x space plus thin space 9.
Comparing space the space equation space with space straight a straight x cubed plus space bx squared space plus space cx space plus thin space straight d comma space we space get
straight a equals 2 comma space straight b space equals space 6 comma space straight c space equals space minus 4 comma space straight d space equals space 9
straight alpha space plus space straight beta space plus space straight gamma equals fraction numerator negative straight b over denominator straight a end fraction equals fraction numerator negative 6 over denominator 2 end fraction equals negative 3
αβγ equals fraction numerator negative straight d over denominator straight a end fraction equals fraction numerator negative 9 over denominator 2 end fraction
Now comma space 1 over αβ plus 1 over βγ plus 1 over αγ equals fraction numerator straight alpha space plus space straight beta space plus space straight gamma over denominator αβγ end fraction equals fraction numerator negative 3 over denominator fraction numerator negative 9 over denominator 2 end fraction end fraction equals 3 cross times 2 over 9 equals 2 over 3
So comma space 1 over αβ plus 1 over βγ plus 1 over αγ equals 2 over 3. end style

Answered by Rebecca Fernandes | 19th Jul, 2016, 09:42: PM