If the sum of two of the roots of ${x^3} + p{x^2} + qx + r = 0$ is zero, then $pq =$

Let $a, b, c, d$ be real numbers such that $|a-b|=2$, $|b-c|=3,|c-d|=4$. Then, the sum of all possible values of $|a-d|$ is

The solution set of the equation $pq{x^2} - {(p + q)^2}x + {(p + q)^2} = 0$ is

If the product of roots of the equation ${x^2} - 3kx + 2{e^{2\log k}} - 1 = 0$ is $7$, then its roots will real when

The number of roots of the equation $\log ( - 2x)$ $ = 2\log (x + 1)$ are

If $a+b+c=1, a b+b c+c a=2$ and $a b c=3$, then the value of $a^{4}+b^{4}+c^{4}$ is equal to $....$