Sum & Product of Roots of a Quadratic Equation

The expression for sum & product of roots of quadratic equation is gotten from the general expression of quadratic equation. If the distinct roots are α and β, then

α + β = -b/a   (sum of roots)

αβ =c/a         (product of roots)

Example 1 – find the sum and products of 2x² + 3x –  1 = 0

Solution

2x² + 3x – 1 = 0

a =2, b = 3, c = -1

Let α and β be the roots of the equation, then

α+β= -b/a= -3/2

αβ = c/a = -1/2

Example 2 – find the sum and products of 3x² – 5x -2 = 0

Solution

3x² -5x -2 =0

a= 3, b= -5, c= -2

let α and β be the roots of the equation, then

α+β= -b/a = 5/3

αβ= c/a= -2/3

NB: The quadratic equation whose root are α and β  is

            (X – α )(X – β) = 0

X² – (α +β)X + αβ = 0

Example – Find the quadratic equation whose roots are 3 & -2

Solution

α=3 and β=-2

α+β = 3 + (-2) = 1

αβ = 3 x -2 = -6

X² – (α +β)x + αβ = 0

X² – (1)X + (-6) = 0

X² – X -6 = 0