Question

if alpha beta are the two zeroes of the polynomial x^2-2x-8 then form a quadratic polynomial whose zeroes are 2alpha and 2beta

Answer 1

hey dear here is your answer
clearly alpha+beta = 2 , alpha × beta = -8
again S= 2 alpha + 2 beta = 2(alpha+beta) = 2(2) = 4
P = 2 alpha × 2 beta = 4( alpha× beta ) = 4 ( -8 ) =-32
therefore , required polynomial is x^2 - Sx + P = x^2 - 4x - 32
hope you like this

Answer 2

Equ -- x^-2x-8
Factorising:
x^-4x+2x-8
x(x-4)+2(x-4)
x=-2 and x=4
A.T.Q
To find a polynomial which satisfy 2 alpha and 2 beta....
2(-2) and 2(4)
alpha=-4 and beta=8 respectively.
Finding sum and product of roots:
alpha+beta=-4+8=
alpha.beta=-4.8=-32
To find polynomial we need sum and product of roots , hence:
x^-(sum of roots)+(product of roots)
x^-4x-32
This the required quadratic polynomial if x^-4x-32
Hope this helped you....