Root of the equation $x^{2}$ - 11x + 22 = 0 are given as 3 and 6.
Let the base of the number be n.
We can get the base of the number easily by two approaches as follows.
1. Sum of the root = -b / a.
Where b and a are the coefficients of the general quadratic equation a$x^{2}$ + bx + c = 0.
Therefore $(3)_{n}$ + $(6)_{n}$ = $(11)_{n}$
$\Rightarrow$ 9 = n + 1
$\Rightarrow$ n = 8.
2. Product of the root = c / a.
So, $(3)_{n}$ $(6)_{n}$ = $(22)_{n}$
$\Rightarrow$ 18 = 2n + 2
$\Rightarrow$ n = 8.
