Question

If alpha and beta are the zeros of the polynomial f(x)=x^2-3x+6 the find the value of 1/alpha+1/beta+alpha^2+beta^2-2 alphabeta

Answer 1

let alpha and beta are zeros of the following polynomial

f(x)=x²-3x+6

by shree dharacharya method-

x=-b±√(b²-4ac)/a2

α=(3+√15 i)/2

β=(3-√15 i)/2

now,

1/α+1/β+α²+β²-2αβ=2/(3+√15 i)+2/(3-√15 i)+(3+√15 i)²/4+(3-√15 i)²/4-2(3+√15 i)(3-√15 i)/4√

1/α+1/β+α²+β²-2αβ=19/2=9.5 ans