Question

if alpha and beta are zeros of the polynomial p(x)=3x^2-5x+6 find alpha^3+beta^3

Answer 1

3x²-5x+6

α+β=5/3

αβ=6/3=2

α³+β³=(α+β)³-3αβ(α+β)
=(5/3)³-3×2×5/3
=125/27-10
=125-270/10
=-14.5

Answer 2

$\textbf{- Answer -}$

The given polynomial is

p (x) = 3x² - 5x + 6

Since α and β are the zeros of p (x),

α + β = - (- 5)/3

⇒ α + β = 5/3 ...(i)

and

αβ = 6/3

⇒ αβ = 2 ...(ii)

Now, α³ + β³

= (α + β)³ - 3αβ (α + β)

= (5/3)³ - (3 × 2 × 5/3)

= 125/27 - 10

= (125 - 270)/27

= - 145/27

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