Question

Use a graphing calculator and a system of equations to find the roots of the equation. x4 − 4x3 = 6x2 − 12x From least to greatest, what are the integral roots of the equation?

Answer 1

The answer is -2 and 0

Answer 2

Roots of equation:
`(-√(3)+3) (0) (-2) (-√(3)-3 )`

Integral roots : -2,0

Explanation:

We have given that equation is
`x^4-4x^3 -6x^2+12x`

now, we solve the equation to find roots

`x^4-4x^3 -6x^2+12x=0`

⇒
`(x) (x+2) (x^2-6x+6)`

we divide
`x^4-4x^3 -6x^2+12x` by
`(x^2-6x+6)`

⇒
`-(-x+√(3)+3) (x+√(3)-3 ) (x) (x+2)`

we can clearly see the two roots through attached graph

From least to greatest :
`(x+2) (x) -(-x+√(3)+3) (x+√(3)-3 )`

Roots of equation:
`(-√(3)+3) (0) (-2) (-√(3)-3 )`

Integral roots : -2,0