Theory question 103
PolynomialsIf α and β are the roots of 3x2 + 5x + 1 = 0, evaluate 27(α3 + β3).
Show the model answer
Model answer
α + β = −5/3, αβ = 1/3.
α³ + β³ = (α + β)³ − 3αβ(α + β) = −125/27 + 5/3 = −80/27.
27(α³ + β³) = −80.
Explanation
Express α³ + β³ using the sum and product of the roots.