If a and b are roots of the quadratic equation 3x^2-6x+2=0.
(i) Find a+b
(ii) Find ab
Anyone can help?
CaptainBlack's method is perfectly acceptable, but there is a general theorem for quadratics you can use to tackle this. (You can actually get theorems for this for higher order polynomials, but I forget the name of the method.)
If you have two roots of a quadratic equation $\displaystyle ax^2 + bx + c = 0$, $\displaystyle r_1~\text{and}~r_2$, then
$\displaystyle r_1 + r_2 = -\frac{b}{a}$
and
$\displaystyle r_1 \cdot r_2 = \frac{c}{a}$
(You can easily get this result by noting that
$\displaystyle r_{1, 2} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ and doing the relevant sum or product of $\displaystyle r_1~\text{and}~r_2$.)
In your particular case, we have a = 3, b = -6, and c = 2. Thus
$\displaystyle r_1 + r_2 = -\frac{-6}{3} = 2$
and
$\displaystyle r1 \cdot r_2 = \frac{2}{3}$
just as CaptainBlack derived.
-Dan