If α and β are the roots of the quadratic equation ax

If α and β are the roots of the quadratic equation ax²+ bx + c = 0, the value of α³ + β³ is

According to question , we can say that
Since α, β are the roots of the quadratic equation
ax²+ bx + c = 0

∴ α + β = −	b	and αβ =	c
	a		a

Now, α³ + β³ = ( α + β )³ - 3αβ( α + β )

=		-	b		³	- 3 x	c	x	- b
			a				a		a

α³ + β³ =	- b³	+	3bc	=	- b² + 3abc
	a³		a²		a³

Hence , α³ + β³ =	b ( 3ac - b² )
	a³