One root of the quadratic equation $x^{2}-5x+6=0$ is $3$. Find the other root.

If the roots of the equation $\frac{\alpha}{x - \alpha} + \frac{\beta}{x - \beta} = 1$ are equal in magnitude but opposite in sign,then $\alpha + \beta = $

Solve the given two equations and select the correct answer from the given options.
$I.$ $7x + 3y = 77$
$II.$ $2x + 5y = (2601)^{1/2}$

If $P(x) = ax^2 + bx + c$ and $Q(x) = -ax^2 + dx + c$ where $ac \neq 0$,then $P(x) \cdot Q(x) = 0$ has at least

If the sum of the roots of the equation $ax^2 + bx + c = 0$ is equal to the sum of their squares,then:

The roots of the quadratic equation $(a + b - 2c)x^2 - (2a - b - c)x + (a - 2b + c) = 0$ are