Question

if alpha and beta are the zeros of the polynomials x²-5x+6 find a polynomial whose zeros are (i)alpha/beta and beta/alpha (ii)alpha+1/alpha-1 and beta+1/beta-1​

Answer 1

x2-5x+6

x2-2x-3x+6=0

x(x-2)-3(x-2)=0

(x-2)(x-3)=0

x=2,x=3

therefore zeroes of polynomial of x2-5x+6 are 2,3

alpha =2and beta3

sum of zeroes alpha +beta =-b/a

2+3=-(-5)/1

5=5

product of zeroes are aplha×beta =c/a

2×3=6

6=6