Question

if alpha and beta are the zeroes of the polynomial 2xsquare-5x+7 then find a quadratic polynomial whose zeroes are 3alpha+4beta and 4 alpha+3beta

Answer 1

Given:--

polynomial equation is--2x^2-5x+7=0.

Therefore,

alpha={5+ix(31)^1/2}/2 &

beta={5-ix(31)^1/2}/2.

Roots of required polynomial are--

(3xalpha+4xbeta,4xalpha+3xbeta)

i.e,

x1={35-i(31)^1/2}/2

& x2={35+i(31)^1/2}/2

Therefore,

the required quadratic polynomial is--

x^2-35x+314.