Formula for Sum and Product of Roots
Sum of Roots: Product of Roots:
From the Quadratic Equation: a = 3, b = 2p and c = -p
a) 2 equal roots.
Let the roots be α & α since the roots are equal . Do note that we can also let the roots be β and β.
Sum of Roots:
Product of Roots:
Substitute Equation (1) into (2)
b) 1 roots is a reciprocal of the other
Let the roots be α & 1/α since the roots are equal . Do note that we can also let the roots be β and 1/β.
Sum of Roots:
There are two unknown variables α and p, we cannot find the value of p, so we try to find for p using product of roots.
Product of Roots:
Students assume that the roots of the equation are always α and β. I purposely posted this solution to show all of you that the roots does not always have to be so.