Explanation

(d)
Let $\alpha\ ,\beta$ are the roots of the equation $x^{2} - ax + b = 0$.
$\therefore\ \alpha + \beta = a$ …(i)
and $\alpha\beta = b$ …(ii)
Roots are prime numbers, so clearly $b$ cannot be a prime number as it is product of two prime numbers [from Eq. (ii)]. Sum of two prime numbers is always an even number except in one situation when one prime number is 2. $`a'$ can be a prime number and can be composite number.
Now, $1 + a + b = 1 + \ \alpha\beta + \alpha + \beta = (1 + \alpha)(1 + \beta)$
$(1 + \alpha),\ (1 + \beta)$ can be prime numbers, can be composite numbers, so $1 + a + b$ is not certain.
So, option (d) is correct.