The equation whose roots are reciprocal of the roots of the equation $3x^2 - 20x + 17 = 0$ is

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 $|\alpha| + |\beta|$ is:

The roots of the quadratic equation $2x^2 + 3x + 1 = 0$ are:

Let $x_1, x_2, x_3 \in R - \{0\}$,$x_1 + x_2 + x_3 \neq 0$ and $\frac{1}{x_1} + \frac{1}{x_2} + \frac{1}{x_3} = \frac{1}{x_1 + x_2 + x_3}$. Then $\frac{1}{x_1^n + x_2^n + x_3^n} = \frac{1}{x_1^n} + \frac{1}{x_2^n} + \frac{1}{x_3^n}$ holds good for:

Given that $x^{3}+y^{3}=72$ and $xy=6$ with $x>y$,then the value of $x-y$ is:

The number of solutions for the equation ${x^2} - 5|x| + 6 = 0$ is