If alpha and beta are the zeroes of the *quadratic polynomial* 2x^2-3x-5, form a quadratic polynomial whose zeroes are:- alpha/(alpha^2+beta^2) ; beta/(alpha^2+beta^2).
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Answer:
zeroes of the polynomial are
-1,2.5
so -1²/-1²+2.5² = 1/7.25
6.25/1+6.25= 6.25/7.25
so polynomial is,
(x-6.25/7.25)(x-1/7.25)
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2x^2+2x-5x-5=0
2x(x+1)+5(x+1)=0
(x+1)(2x+5)=0
x=-1. x=-5/2
-1/(1+25/4)= -1/(29/4)= -4/29
-5/2/(1+25/4) =-5/2/(29/4) =-10/29
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