Question

if alpha and beta are the zeros of the polynomial x square - 3 x + 2 then find the value of Alpha Cube + beta cube

Answer 1

3divided by 2 alpha +beta =3 divided by 2

Answer 2

hello friends...

here given that
alpha and beta are roots of the equation
x² -3x +2

solution :-
we know that
the sum of roots = -b/a = coefficient of x / constant term

and
the product of alpha and beta = c/a = coefficient of x ² / constant term

here
alpha+ beta = -b/a = -(-3) /1 = 3
and
alpha× beta = c/a = 2/1 = 2

now
α +β = 3 & αβ =2,

we have to find
α³ + β³ = ?

we know that
a³+ b³ = (a+b)³ - 3ab(a+b)

=> α³ +β³ = (α+β)³ -3αβ(α+β)
= 3³ - 3 ×2×3 = 27 - 18 = 9 answer

♦ hope it helps ♦