If one root of the equation $x(x + 2) = 3 - ax^2$ approaches infinity,then the value of $a$ approaches which of the following?

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

If the roots of the equation $x^2 - (3k - 1)x + 2k^2 + 2k = 0$ are equal,then the value of $k$ will be .....

$\alpha, \beta, \gamma, 2, \varepsilon$ are the roots of the equation $x^5+4 x^4-13 x^3-52 x^2+36 x+144=0$. If $\alpha < \beta < \gamma < 2 < \varepsilon$,then find the value of $\alpha+2 \beta+3 \gamma+5 \varepsilon$.

Let $f(x)$ be a polynomial and $a, b$ be distinct real numbers. Then the remainder in the division of $f(x)$ by $(x-a)(x-b)$ is

The roots of the equations $2x^2 - 5x + 1 = 0$ and $x^2 + 5x + 2 = 0$ are: