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.