The sum of squares of the roots of the equation $x^{2/3} + x^{1/3} - 2 = 0$ is

The polynomial equation of degree $4$ having real coefficients with three of its roots as $2 \pm \sqrt{3}$ and $1+2i$ is:

Let $S = \{x^{3} + ax^{2} + bx + c : a, b, c \in \mathbb{N} \text{ and } a, b, c \le 20\}$ be a set of polynomials. Then the number of polynomials in $S$, which are divisible by $x^{2} + 2$, is

In the real number system,the equation $\sqrt{x+3-4 \sqrt{x-1}}+\sqrt{x+8-6 \sqrt{x-1}}=1$ has

Which of the following is not a root of $f(x) = x^3 - 11x^2 + 36x - 36$?

If the roots of the equation $({p^2} + {q^2}){x^2} - 2q(p + r)x + ({q^2} + {r^2}) = 0$ are real and equal,then $p, q, r$ will be in: