1. ©G Dear2008 – Not to be sold/Free to use
General Mathematic
(Preliminary)
Quadratics
Sum and Products
of Roots
Stage 6 - Year 11
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©G Dear2008 – Not to be sold/Free to use

2. Sum and Product of Roots
The general quadratic equation can be written as x2 - (α + β)x + αβ = 0
where α and β are the roots of the equation.
If α and β are the roots of ax2 + bx + c = 0. a -b
Sum of roots: α + β = a c
Product of roots: αβ =

3. Sum and Product of Roots
Find α + β and αβ if α and β are the roots of
2x2 – 3x – 6 = 0 c a -6 2
Product of roots: αβ = =
= -3 -b a
-(-3) 2
Sum of roots: α + β = =
= 1.5

4. Sum and Product of Roots
If you know the roots:
α = 2
β = -3
x2 – (α + β)x + αβ = 0
x2 - (2 + –3)x + 2 x –3 = 0
x2 + x – 6 = 0

5. Sum and Product of Roots
Find α + β and αβ if α and β are the roots of
2x2 – 3x – 6 = 0
–(–3) ± (–3)2 – 4 x 2 x (–6)
2 x 2
x =
3 ± 4
x =
3 ± 57 4 = 4
3 – 57 x
αβ = 4
α + β =
3 – 57 +
= = = 1.5
6 3
4 2
= = -3 =
9 – 16