Question

What are the roots of the polynomial equation? 0= x^4-3x^3+10x^2-24x+16
(Please show steps)

Answer 1

1, 2, 2i
`√(2)`, -2i
`√(2)`

Explanation:

Answer 2

The roots of the polynomial are ( x - 1 ) ( x - 2 ) ( x² + 8 ) .

Explanation:

Given polynomial-

`x^(4) - 3 x^(3) + 10 x^(2) - 24 x + 16 = 0`

`( x^(4) + 10 x^(2) + 16) - 3 x^(3) - 24 x = 0`

`(x^(4) + 8 x^(2) + 2 x^(2)  + 16) - 3 x ( x^(2)  + 8 ) = 0`

`x^(2) ( x^(2) + 8) + 2 ( x^(2)  + 8 ) - 3 x ( x^(2) + 8 ) = 0`

`[ ( x^(2) + 8 ) ( x^(2) + 2 - 3 x = 0 )`

`[ (x^(2) + 8) (x^(2) - 3 x + 2 ) ] = 0`

`[ (x^(2) + 8) (x^(2) - 2 x - x + 2 ) ] = 0`

`( x^(2)  + 8) [x( x - 2 ) - 1 ( x - 2 )  ] = 0`

`(x^(2) + 8 ) ( x - 2 ) ( x - 1 ) = 0`

`(x - 1 ) ( x - 2 ) ( x^(2) + 8 )`