If $p$ and $q$ are the roots of $x^2 + px + q = 0$,then

The value of $a$ such that the sum of the squares of the roots of the equation $x^2 - (a - 2)x - a + 1 = 0$ assumes the least value is:

If $\alpha, \beta, \gamma$ are the roots of $f(x) = x^3 - 9x^2 + 26x - 24$,then $\frac{1}{\alpha}, \frac{1}{\beta}, \frac{1}{\gamma}$ are the roots of which equation?

Let $p(x)$ be a quadratic polynomial with constant term $1$. Suppose $p(x)$,when divided by $x-1$,leaves remainder $2$ and when divided by $x+1$,leaves remainder $4$. Then,the sum of the roots of $p(x)=0$ is

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

If $-1$ is a twice repeated root of the equation $ax^3+bx^2+cx+1=0$,then