If alpha and beta are the zeroes of the polynomial 6y(squared)+7y+2 , find quadratic    polynomial , whose zeroes are 1/ alpha and 1/ beta ?

Asked by suresh bhaskar | 9th Jul, 2016, 02:20: PM

Expert Answer:

begin mathsize 12px style Given space that space straight alpha space and space straight beta space are space the space zeroes space of space the space polynomial space 6 straight y squared plus 7 straight y plus 2.
rightwards double arrow straight alpha plus straight beta equals fraction numerator negative 7 over denominator 6 end fraction space and space αβ equals 2 over 6 equals 1 third
Now comma sum space of space the space zeroes equals space 1 over straight alpha plus 1 over straight beta equals fraction numerator straight alpha plus straight beta over denominator αβ end fraction equals fraction numerator fraction numerator negative 7 over denominator 6 end fraction over denominator 1 third end fraction equals fraction numerator negative 7 over denominator 2 end fraction
product space of space the space zeroes equals 1 over straight alpha 1 over straight beta equals 1 over αβ equals 3
So comma space the space required space polynomial space is comma
straight y squared minus left parenthesis sum space of space the space zeroes right parenthesis straight y space plus product space of space the space zeroes
equals straight y squared plus 7 over 2 straight y plus 3
end style

Answered by Rebecca Fernandes | 9th Jul, 2016, 06:08: PM

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