QUESTIONS ON POLYNOMAIL EQUATION

Problem 1 :

If p and q are the roots of equation lx² + nx + n = 0, show that √(p/q) + √(q/p) + √(n/l) = 0

Solution :

p and q are roots of the equation.

p + q = -n/l and pq = n/l

Problem 2 :

If the equations x² + px + q = 0 and x² + p'x + q' = 0 have a common root, show that it must be equal to 

Solution :

Problem 3 :

A 12 meter 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.

Solution :

Length of the tree is 12 m.

Let x be the length of the tree to be cut out.

Length of the part of the tree left standing = 12 - x

x = ∛(12-x)

Take cube on both sides.

x³ = 12 - x

x³ + x - 12 = 0