If $\alpha$ and $\beta$ are the roots of the equation $ax^2 - bx - c = 0$,then $\alpha^2 - \alpha\beta + \beta^2 = .......$

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?

For the equation $\frac{1}{x + a} - \frac{1}{x + b} = \frac{1}{x + c}$,if the product of the roots is zero,what is the sum of the roots?

If $\alpha \ne \beta$ but $\alpha^2 = 5\alpha - 3$ and $\beta^2 = 5\beta - 3$,then the equation whose roots are $\frac{\alpha}{\beta}$ and $\frac{\beta}{\alpha}$ is

If the sum of two of the roots of $x^3+p x^2-q x+r=0$ is zero,then $pq$ is equal to

What is the sum of the squares of the roots of the equation $x^2 - 3x + 1 = 0$?