For the quadratic equation $4x^2 + 3x + 7 = 0$,if $\alpha$ and $\beta$ are the roots,then find the value of $1/\alpha + 1/\beta$.

If $\alpha$ and $\beta$ $(\alpha < \beta)$ are the roots of the equation $x^2 + bx + c = 0,$ where $c < 0 < b,$ then

If $\alpha$ and $\beta$ are the roots of the quadratic equation $x^2 - 3x + 5 = 0$,then find the quadratic equation whose roots are $(\alpha^2 - 3\alpha + 7)$ and $(\beta^2 - 3\beta + 7)$.

Let $\alpha$ and $\beta$ be the roots of $x^{2}-6x-2=0$. If $a_{n}=\alpha^{n}-\beta^{n}$ for $n \geq 1$,then the value of $\frac{a_{10}-2a_{8}}{3a_{9}}$ is ..... .

If $\alpha, \beta$ are the roots of $a x^2+b x+c=0$,then the quadratic equation whose roots are $\sqrt{5} \alpha, \sqrt{5} \beta$ is

If $\alpha, \beta$ are the roots of $x^2+p x+q=0$,then the values of $\alpha^3+\beta^3$ and $\alpha^4+\alpha^2 \beta^2+\beta^4$ are respectively ...... and ......