Question

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

Answer 1

Answer:

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

Step-by-step explanation:

Given polynomial-

$x^{4} - 3 x^{3} + 10 x^{2} - 24 x + 16 = 0$

$( x^{4} + 10 x^{2} + 16) - 3 x^{3} - 24 x = 0$

$(x^{4} + 8 x^{2} + 2 x^{2}  + 16) - 3 x ( x^{2}  + 8 ) = 0$

$x^{2} ( x^{2} + 8) + 2 ( x^{2}  + 8 ) - 3 x ( x^{2} + 8 ) = 0$

$[ ( x^{2} + 8 ) ( x^{2} + 2 - 3 x = 0 )$

$[ (x^{2} + 8) (x^{2} - 3 x + 2 ) ] = 0$

$[ (x^{2} + 8) (x^{2} - 2 x - x + 2 ) ] = 0$

$( x^{2}  + 8) [x( x - 2 ) - 1 ( x - 2 )  ] = 0$

$(x^{2} + 8 ) ( x - 2 ) ( x - 1 ) = 0$

$(x - 1 ) ( x - 2 ) ( x^{2} + 8 )$

Answer 2

Answer:

1, 2, 2i$\sqrt{2}$, -2i$\sqrt{2}$

Step-by-step explanation: