Question

If alpha +beta=5 and alpha cube+beta cube=35 find the quadratic equation whose root are alpha and beta

Answer 1

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Answer 2

quadratic equation is x² - 5x + 6

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

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