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CBSE Class 10 Answered

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 | 09 Jul, 2016, 02:20: PM
answered-by-expert 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 | 09 Jul, 2016, 06:08: PM

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