An cubic equation is an equation which can be represented in the form , where can be any number (may be complex if given so) where .
An cubic equation has roots (solutions), may be equal or not equal.
Relation between coefficients and roots:
For an cubic equation , let and be its roots, then:
|Root expression||Equals to|
Given that, and are its roots, then is the required cubic equation. Since it can be represented in the form , we have the following approach:
Now comparing this with , we have:
Find the sum of the squares of the roots of the cubic equation .
Representing it in the form .
Recall that (This is an algebraic identity and not related solely to cubic equations).
From the relations between the coefficients and its roots, we have and .
Plugging it in the relation, we have