Question

Find the quadratic equation Sum of whose roots is 3 and the Sum of the cubes of roots is 7.

Answer 1

Step-by-step explanation:

Let the roots be α and β

The sum of the root is 3 :

α + β = 3 ------------------ [ 1 ]

The sum of the cubes of the roots is 7 :

α³ + β³ = 7

(α + β)³ -3αβ(α + β) = 7-------------------- [ 2 ]

Subtract [ 1 ] into [ 2 ] :

(3)³ - 3αβ(3) = 7

27 - 9αβ = 7

9αβ = 20

αβ = 20/9

So we know that :

Sum of roots = α + β = 3

Product of the roots = αβ = 20/9

From the quadratic equation :

x² - (α + β) x + αβ = 0

x² - 3x + 20/9 = 0

9x² - 27x + 20 = 0

Answer: 9x² - 27x + 20 = 0