What is the remainder of $2x^3 - 5x^2 + 7$ when divided by $(x - 2)$?

The roots of $4x^2 + 6px + 1 = 0$ are equal,then the value of $p$ is

If the roots of the equation $(m - n)x^2 + (n - l)x + (l - m) = 0$ are equal,then which of the following is true for $l, m,$ and $n$?

The roots of the given equation $2(a^2 + b^2)x^2 + 2(a + b)x + 1 = 0$ are

Let $a, b \in \mathbb{R}, a \neq 0$ be such that the equation $a x^{2}-2 b x+5=0$ has a repeated root $\alpha,$ which is also a root of the equation $x^{2}-2 b x-10=0$. If $\beta$ is the other root of this equation,then $\alpha^{2}+\beta^{2}$ is equal to:

If $k \in R$,then the roots of $(x-2)(x-3)=k^2$ are always