The common root of the equations $x^{2}-7x+10=0$ and $x^{2}-10x+16=0$ is:

The number of solutions of $\frac{\log 5 + \log (x^2 + 1)}{\log (x - 2)} = 2$ is

Let one root of the equation $ax^{2} + bx + c = 0$ be $\alpha$. Then the other root is $2\alpha$. Find the relation between $a, b,$ and $c$.

The roots of the equation $3^{2x} - 10 \cdot 3^x + 9 = 0$ are

Find the quadratic equation whose roots are reciprocals of the roots of the equation $3x^{2}-20x+17=0$.

The number of real roots of the equation $5 + |2^x - 1| = 2^x(2^x - 2)$ is