Use the expression 3x4 x3 29x2 x 24 to a List all of the

Use the expression 3x^4 - x^3 - 29x^2 + x - 24 to: a. List all of the possible zeros of the polynomial b. write the polynomial as the product of a linear write the expression in standard form.

Solution

Solution:

Here;

3x^4 – x^3 – 29x^2 + x – 24 = 0

b)

=> 3 *(x +3.095) *(x -3.376) *(x^2 -0.052*x +0.766) = 0

=> 3 *(x +3.095) *(x -3.376) *(x +(-0.026+i*0.875)) *(x +(-0.026-i*0.875)) = 0

a)

3 *(x +3.095) *(x -3.376) *(x +(-0.026+i*0.875)) *(x +(-0.026-i*0.875)) = 0

Hence,

(x +3.095) = 0 --eq1

(x -3.376) = 0 --eq2

(x +(-0.026+i*0.875)) = 0 --eq3

and

(x +(-0.026-i*0.875)) = 0 ---eq4

=> x = -3.095 , 3.376 , 0.026 - 0.875i , 0.026 + 0.875i