Let $p, q, r \in \mathbb{R}$ and $r > p > 0$. If the quadratic equation $px^2 + qx + r = 0$ has two complex roots $\alpha$ and $\beta$,then what is the value of $|\alpha| + |\beta|$?

If the graph of $y = ax^3 + bx^2 + cx + d$ is symmetric about the line $x = k$,then:

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

Let $p(x) = x^2 - 5x + a$ and $q(x) = x^2 - 3x + b$,where $a$ and $b$ are positive integers. Suppose $\text{HCF}(p(x), q(x)) = x - 1$ and $k(x) = \text{LCM}(p(x), q(x))$. If the coefficient of the highest degree term of $k(x)$ is $1$,then the sum of the roots of $(x - 1) + k(x)$ is:

The product of the roots of the equation $9x^{2}-18|x|+5=0$ is

If the roots of the equation $bx^2 + cx + a = 0$ are imaginary,then for all real values of $x,$ the expression $3b^2x^2 + 6bcx + 2c^2$ is :