If α, β, and γ are the roots of the equation x³ + px² + qx + r = 0, find the value of  \(\Sigma \frac { 1 }{ \beta \gamma } \) in terms of the coefficients.

Construct a cubic equation with roots 1, 2 and 3

If α, β, γ  and \(\delta\) are the roots of the polynomial equation 2x⁴ + 5x³ − 7x² + 8 = 0, find a quadratic equation with integer coefficients whose roots are α + β + γ + \(\delta\) and αβ૪\(\delta\).

Formulate into a mathematical problem to find a number such that when its cube root is added to it, the result is 6.

A 12 metre tall tree was broken into two parts. It was found that the height of the part which was left standing was the cube root of the length of the part that was cut away. Formulate this into a mathematical problem to find the height of the part which was left standing.