Expected value of random variable

[lollipop2046]

I am asked to show that the distribution of a random variable X with possible values 0,1,2 is determined by mu_1 = E(X) and mu_2 = E(X^2), by finding a formula for P(X=x) in terms of mu_1 and mu_2, x=0, 1, 2.

I don't really see why E(X^2) is involved as I thought all we need is just the basic definition of expectation ofa random variable X which is the summation of xP(X=x) for all x..

can anyone please help me?