Verify that the numbers given alongside the cubic polynomials below are their zeroes. Also,verify the relationship between the zeroes and the coefficients in each case: $x^{3}-4x^{2}+5x-2; 2, 1, 1$.

(A) Let the polynomial be $p(x) = x^{3} - 4x^{2} + 5x - 2$.
The given numbers are $2, 1, 1$.
For $x = 2$: $p(2) = (2)^{3} - 4(2)^{2} + 5(2) - 2 = 8 - 16 + 10 - 2 = 0$.
For $x = 1$: $p(1) = (1)^{3} - 4(1)^{2} + 5(1) - 2 = 1 - 4 + 5 - 2 = 0$.
Since $p(2) = 0$ and $p(1) = 0$,the numbers $2, 1, 1$ are indeed the zeroes of the polynomial.
Comparing $p(x)$ with the standard form $ax^{3} + bx^{2} + cx + d$,we get $a = 1, b = -4, c = 5, d = -2$.
Verification of relationships:
$1$. Sum of zeroes: $2 + 1 + 1 = 4 = -(-4)/1 = -b/a$.
$2$. Sum of product of zeroes taken two at a time: $(2)(1) + (1)(1) + (2)(1) = 2 + 1 + 2 = 5 = 5/1 = c/a$.
$3$. Product of zeroes: $2 \times 1 \times 1 = 2 = -(-2)/1 = -d/a$.
Thus,the relationship between the zeroes and the coefficients is verified.