Question

select all zeros of the polynomial function. \\( g(x) = x^4 - 9x^2 - 4x + 12 \\)

Explanation:

Step1: Test x=-3 for root

$g(-3)=(-3)^4 - 9(-3)^2 -4(-3)+12=81-81+12+12=24
eq0$

Step2: Test x=-2 for root

$g(-2)=(-2)^4 - 9(-2)^2 -4(-2)+12=16-36+8+12=0$

Step3: Test x=-1 for root

$g(-1)=(-1)^4 - 9(-1)^2 -4(-1)+12=1-9+4+12=8
eq0$

Step4: Test x=1 for root

$g(1)=(1)^4 - 9(1)^2 -4(1)+12=1-9-4+12=0$

Step5: Test x=2 for root

$g(2)=(2)^4 - 9(2)^2 -4(2)+12=16-36-8+12=-16
eq0$

Step6: Test x=3 for root

$g(3)=(3)^4 - 9(3)^2 -4(3)+12=81-81-12+12=0$

Step7: Test x=4 for root

$g(4)=(4)^4 - 9(4)^2 -4(4)+12=256-144-16+12=108
eq0$

Step8: Test x=5 for root

$g(5)=(5)^4 - 9(5)^2 -4(5)+12=625-225-20+12=392
eq0$

Answer:

-2, 1, 3