Question

if alpha and beta are the zeros of f(x) = x*2-1 find quadratic polynomial whose zeros are 2alpha÷beta and 2beta÷alpha

Answer 1

=x²-1²=(x+1)(x-1)
⇒x+1=0                 or                                  ⇒x-1=0
⇒x=-1                     or                                 ⇒x=1
here α= -1               β=1
zeroes of the quadratic polynomial=
⇒2α/β=2(-1)/1= -2
⇒2β/α=2(1)/(-1)= -2
⇒k(x²-(α+β)x+(αβ))
⇒k(x²-(-2)x+(-2)
⇒k(x²+2x-2)
here k=1
and the quadratic polynomial is x²+2x-2