Question

If alpha and beta are the zeros of quadratic polynomial p(x) =x^2-5x+6 , find a quadratic polynomial whose roots are alpha-1/alpha+1 , beta-1/beta+1.

Answer 1

Answer:

Step-by-step explanation:

x2-5x+6=0

x2-3x-2x+6=0

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

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

The zeroes are 2,3.

So,

alpha-1=2-1=1

alpha+1=2+1=3

alpha-1/alpha+1=1/3

beta-1=3-1=2

beta+1=3+1=4

beta-1/beta+1=2/4=1/2

sum of roots=1/3+1/2=5/6

product=1/3*1/2=1/6

formula=k(x2-(sum of roots) +product)

k(x2-(5/6)x+1/6)

k=6,so

6x2-5x+6=p(x)