Question

ifα,β are zeroes of the polynomial p(x)=3x²-2x-6,then find α³+ β³​

Answer 1

by heart the formula for (alpha)^3+(beta)^3

Answer 2

Answer:

116/27

Step-by-step explanation:

as given : 3x² - 2x - 6

we have

$\alpha + \beta = - b \div a$

$\alpha \beta = c \div a$

now,

$(\alpha + \beta) {}^{2} = \alpha {}^{2} + \beta {}^{2} + 2 \alpha \beta$

(-(-2/3))² = a² + b² + 2( -6/3 )

(4/9) = a² + b² - 4

40/9 = a² + b²

now , using formula a³ + b³ = (a+b) (a²-ab+b²)

=> a³+b³= (2/3)(40/9 - (-6/3) )

=> a³+b³= (2/3)(40/9+2)

=> a³+b³= (2/3)(58/9)

=> a³+b³= (116/27)