Question

Find the equation whose roots are the cubes of the roots of x+3x²+2 =0.​

Answer 1

Answer:

9x²-6x+4

Step-by-step explanation:

3x²+x+2=0

Let the roots be a,b

a+b=-1/3 ab=2/3

a²+b²=(a+b)²-2ab

a²+b²=(-1/3)²-2(2/3)

a²+b²=1/9-4/3

a²+b²= -11/9

a²+b²-ab= -11/9-2/3= -18/9

a²+b²-ab= -2

a³+b³=(a+b)(a²+b²-ab)= -1/3(-2)

a³+b³=2/3

Now the roots are cubed

Then roots are a³ and b³

Equation is

x²-(a³+b³)x+a³b³=0

x²-2/3(x)+(2/3)²=0

x²-2/3x+4/9=0

9x²-6x+4=0