Are the following statements 'True' or 'False'? Justify your answers.
If all the zeroes of a cubic polynomial are negative,then all the coefficients and the constant term of the polynomial have the same sign.

(A) The statement is True.
Let the cubic polynomial be $f(x) = a(x - \alpha)(x - \beta)(x - \gamma)$,where $\alpha, \beta, \gamma < 0$ are the negative zeroes.
Let $\alpha = -p, \beta = -q, \gamma = -r$,where $p, q, r > 0$.
Then $f(x) = a(x + p)(x + q)(x + r)$.
Expanding this,we get $f(x) = a[x^3 + (p + q + r)x^2 + (pq + qr + rp)x + pqr]$.
Comparing this with the standard form $f(x) = ax^3 + bx^2 + cx + d$,we get:
$b = a(p + q + r)$
$c = a(pq + qr + rp)$
$d = a(pqr)$
Since $p, q, r > 0$,the terms $(p + q + r)$,$(pq + qr + rp)$,and $(pqr)$ are all positive.
Therefore,$a, b, c,$ and $d$ all have the same sign as $a$.