Question

plz answer fast if alpha and beta are zeroes of the polynomial xsq-2x-8 then form a quadratic polynomial whose zeros are 2alpha and 2beta

Answer 1

α=-2×2
  =-4
β=-8×2
  =-16
to form q.p=x^2-sum of x + product
                 =x^2-4x-16.

Answer 2

= p(x) = x2-2x-8

= sum of zeroes = α+β

= -b/a = 2/1 = 2................(1)

= products or zeros = αβ

= c/a = -8/1 = -8.................(2)

= Given zeros are 2α and 2β,

= sum of zeroes = 2α+2β

= 2(α+β)

= 2 . 2 = 4. (using (1))

= product of zeroes = 2α . 2β

= 4αβ = 4 . -8 = -32..................(using(2))

= the required polynomial ,

=p(x) x2-4x-32.