Posted by **echo** on Thursday, June 7, 2012 at 9:35am.

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

- maths -
**MathMate**, Thursday, June 7, 2012 at 10:31am
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.

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