Question

if alpha and beta are the zeros of the polynomial 2x^2-4x+5 then find the values of
(i)alpha^2+beta^2
(ii)1/alpha^2+1/beta^2
(iii)(r)alpha/beta+(r)beta/alpha
(iv)alpha^-1+beta^-1

Answer 1

The general solution to the equation
ax^2+bx+c=0
is, using the quadratic formula:
α=(-b+√(b²-4ac))/2a, and
β=(-b-√(b²-4ac))/2a

From there, expand α²+β² to get (b²-2ac)/a²

I will leave parts (ii) to (iv) for you as practice.

Answer 2

alpha+beta=-b/a
=--4/2
=2
alpha^2+beta^2=(alpha+beta)^2
=2^2
=4

(ii)take reciprocal(1/2)^2=1/4
(iv)a^-1=1/a similarly 1/2

tried my best to answer hope its correct:)
your pal
mathew