Algebra · SS 1
Sum and product of roots
Find the sum and product of the roots without solving, or build an equation from its roots.
- α + β = −ba
- αβ = ca
What the letters mean
- α, β
- the two roots (alpha and beta)
- a, b, c
- the numbers in ax2 + bx + c = 0
Worked example
For 2x2 − 7x + 3 = 0, find the sum of the roots.
Step 1: a = 2, b = −7
α + β = −(−7)2 = 72 = 3.5
Step 2: Check by solving
The roots are 3 and 12, and 3 + 0.5 = 3.5 ✓
Final answer: 3.5
An equation with roots α and β is x2 − (α + β)x + αβ = 0.
See it
Play with this picture from the Quadratic Equations by Factorisation lesson.
y = x2 − x − 6
x2 − x − 6 = (x + 2)(x − 3)
Roots: x = −2 or x = 3
Check: −2 + 3 = 1 (that's −b) and −2 × 3 = −6 (that's c)
b (the x number)−1
c (the number)−6