Question

if alpha and beta are the zeros of the polynomial f(x)=ax squared +bx+c than find the value of alpha square and beta square and 1/alpha +beta/alpha,alpha cubic +beta cubic , alpha square /beta +beta square /alpha

Answer 1

Step-by-step explanation:

f(x) = ax² +bx +c

\alpha + \beta = -b/a

\alpha\beta = c/a

\alpha² + \beta²

(a+b)² = a² +b² +2ab

(-b/a)². = \alpha² +\beta² +2(c/a)

= b²/a² -2c/a

= b²- 2ca/a²

\alpha² +\beta² = b²- 2ca/a²

\alpha³ + \beta³

(a+b)³ = a³ +b³ + 3ab ( a+b)

(-b/a)³ = \alpha³ +\beta³ + 3 (c/a)(-b/a)

-b³/a³ = \alpha³+ \beta³ -3cb / a²

-b³/ a³ +3cb /a²

= -b³ + 3cba /a³

\alpha³ + \beta³= -b³ + 3cba /a³