If one of the roots of the equation $6x^3-25x^2+2x+8=0$ is an integer and $\alpha > 0$,$\beta < 0$ are the other two roots,then $\frac{4}{\alpha}+\frac{1}{\beta}=$

The solution of the equation $2x^3 - x^2 - 22x - 24 = 0$,given that two of the roots are in the ratio $3:4$,is:

If $\frac{k}{kx+3}+\frac{3}{3x-k}=\frac{12x+5}{(kx+3)(3x-k)}$ for all $x \in R - \{-\frac{3}{k}, \frac{k}{3}\}$,then both the roots of the equation $kx^2-7x+3=0$ are

Let $\alpha, \beta$ be two roots of the quadratic equation $x^2+ax-b=0, b \neq 0$. If the straight line $x \cos \theta + y \sin \theta = c$ touches the curve $(\frac{x}{\alpha})^n + (\frac{y}{\beta})^n = 2$ at the point $(\alpha, \beta)$, then $(\frac{a}{b})^2 + \frac{2}{b} =$

If $f(x) = x^2 + bx + c$ and $f(1+k) = f(1-k)$ for all $k \in R$,for two real numbers $b$ and $c$,then:

For what values of $k$ will the equation $x^2 - 2(1 + 3k)x + 7(3 + 2k) = 0$ have equal roots?