Question
Thu April 03, 2014 By: Sanjay Padmanabhan

if the product of two zeros of the polynomial p(x)=2xcube+6xsquare-4x+9is3 then its third zero is

Expert Reply
Thu April 03, 2014
Let alpha comma beta comma gamma, be the three zeros of the given polynomial P open parentheses x close parentheses equals 2 x cubed plus 6 x squared minus 4 x plus 9
Also given that the product of two zeros of the above polynomial is 3
 
T h a t space i s space alpha cross times beta equals 9
From the given equation, product of all the three zeros is alpha cross times beta cross times gamma equals fraction numerator minus d over denominator a end fraction equals fraction numerator minus 9 over denominator 2 end fraction
Then
fraction numerator minus 9 over denominator 2 end fraction equals 3 cross times gamma rightwards double arrow gamma equals fraction numerator minus 3 over denominator 2 end fraction
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