# ©G Dear2008 – Not to be sold/Free to use

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

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 =

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

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

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