Let $a, b, c$ be three real numbers such that $a + 2b + 4c = 0$. Then the equation $ax^2 + bx + c = 0$

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:

If the roots of the equation $x^2 - bx + c = 0$ are two consecutive integers,then $b^2 - 4c = ......$

The sum of all non-integer roots of the equation $x^5-6x^4+11x^3-5x^2-3x+2=0$ is

How many roots does the equation $x - \frac{2}{x - 1} = 1 - \frac{2}{x - 1}$ have?

If $1-i$ is a root of the equation $x^2+ax+b=0$,then $b$ is equal to