If alpha and beta are zeroes of the quadratic polynomial x2-5x+4, then find all the quadratic polynomials whose zeroes are alpha+1/beta and beta+1/alpha.

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Solution

p(x)=x2-4x-x+4=0
x(x-4)-1(x-4)=0
(x-4)(x-1)=0
Therefore x=4 and x=1
So, alpha=4 nd beta

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