If $\alpha, \beta, \gamma$ are the roots of the equation $3x^3 - 9x^2 + 5x - 7 = 0$,then what is the value of $\alpha + \beta + \gamma$?

Two roots of the cubic equation $x^3 + 3x^2 + kx + 12 = 0$ are real and unequal but have the same absolute value. Find the value of $k$.

If $\alpha, \beta, \gamma$ are the roots of the equation $4x^3 + 12x^2 - 7x + 165 = 0$ and $\alpha + 5, \beta + 5, \gamma + 5$ are the roots of the equation $ax^3 + bx^2 + cx + d = 0$,then the product of the roots of the second equation is:

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

The roots of the equation $x^2 + bx - c = 0$ where $b, c > 0$ are:

For the equation $3x^2 + px + 3 = 0, p > 0$,if one of the roots is the square of the other,then $p$ is equal to: