Question

Sum of the roots of the quadratic equation is 5 and sum of their cubes is 35, then find the quadratic equation

Answer 1

Let α and β be the roots of the quadratic equation.

According to the given conditions,

α + β = 5 and α³ + β³ = 35

Now, (α + β)³ = α³ + 3α²β + 3αβ² + β³

∴ (α + β)³ = α³ + β³ + 3αβ(α + β)

∴ (5)³ = 35 + 3αβ(5)

∴ 125 = 35 + 15αβ

∴ 125 – 35 = 15αβ

∴ 15αβ = 90

∴ αβ = `90/15`

∴ αβ = 6

∴ The required quadratic equation is

x² − (α + β)x + αβ = 0

∴ x² − 5x + 6 = 0