Question

in the quadratic equation if the roots of alpha + beta is equals to 5 and Alpha into beta is equals to 6 then what is alpha cube and Beta cube?​

Answer 1

It is given that,

α + β = 5 and α³ + β³ = 35

then we have to find the quadratic equation whose roots are α and β.

as α³ + β³ = 35

⇒(α + β)³ - 3αβ(α + β) = 35

⇒(5)³ - 3αβ(5) = 35

⇒125 - 35 = 15αβ

⇒90 = 15αβ

⇒αβ = 6

Now, quadratic equation is given

x² - (sum of roots)x + product of roots

⇒x² - (α + β)x + αβ

⇒x² - 5x + 6

Thus, α³ + β³ = 35 according to the question is the answer.

HOPE IT HELPS YOU BUDDY.