If the product of the roots of the equation $x^2 - 3kx + 2e^{2\log k} - 1 = 0$ is $7$,then find the value of $k$.

If the roots of the given equation $(2k + 1)x^2 - (7k + 3)x + k + 2 = 0$ are reciprocal to each other,then the value of $k$ will be

If $\alpha, \beta$ are the roots of $x^2 - 2x + 4 = 0$,then $\alpha^5 + \beta^5$ is equal to

The values of $b$ and $c$ for which the identity $f(x+1)-f(x)=8x+3$ is satisfied,where $f(x)=bx^2+cx+d$,are

If $\alpha, \beta, \gamma$ are roots of $x^3 - 2x^2 + 3x - 2 = 0$,then the value of $\left( \frac{\alpha \beta}{\alpha + \beta} + \frac{\alpha \gamma}{\alpha + \gamma} + \frac{\beta \gamma}{\beta + \gamma} \right)$ is

If $\alpha, \beta, \gamma$ are the roots of $x^3+p x^2+q x+r=0$,then $\alpha^3+\beta^3+\gamma^3=$