Question

Please reply fast .
Thnx a lot to the helper!

Answer 1

19.Let alpha=a and beta=b
Then,
a+b=2
ab=1

Relationship between Zeroes of new polynomial
Sum of zeroes =2a/b+2b/a
=(2a^2+2b^2)/ab
={2 (a^2+b^2)}/1 [ab=1]
=[2 {(a+b)^2-2ab}]
=[2 {2}^2-2×1}]
=[2 {4-2}]
=2×2=4
Product of zeroes = 2a/b×2b/a
=4ab/ab
=4
So new polynomial is
x^2-(sum of zeroes)x+(product of zeroes)
=x^2-4x+4