If $\alpha$ and $\beta$ are the roots of the equation $4x^2 + 3x + 7 = 0$,then $\frac{1}{\alpha} + \frac{1}{\beta} = $

If $\alpha, \beta$ and $\gamma$ are the roots of the equation $2x^3+3x^2-5x-7=0$,then $\frac{1}{\alpha^2}+\frac{1}{\beta^2}+\frac{1}{\gamma^2}=$

The equation whose roots are the reciprocals of the roots of the equation $3x^2 - 20x + 17 = 0$ is

If $\alpha$ and $\beta$ are the roots of the equation $2x^2 - 35x + 2 = 0$,then the value of $(2\alpha - 35)^3 \cdot (2\beta - 35)^3$ is equal to

Sachin and Rahul solve a quadratic equation. Sachin makes a mistake in writing the constant term and obtains roots $(4, 3)$. Rahul makes a mistake in writing the coefficient of $x$ and obtains roots $(3, 2)$. What are the correct roots of the equation?

If $\alpha, \beta, \gamma$ are the real roots of the equation $x^3 - 3px^2 + 3qx - 1 = 0$,then find the centroid of the triangle whose vertices are $(\alpha, \frac{1}{\alpha}), (\beta, \frac{1}{\beta})$ and $(\gamma, \frac{1}{\gamma})$.