Answer:
The zeros of the given polynomial function are
2,2,[tex]\pm\sqrt{5}[/tex]
Step-by-step explanation:
Given polynomial is [tex]P(x)=x^4-4x^3-x^2+20x-20[/tex]
To find the zeros equate the given polynomial to zero
ie., P(x)=0
[tex]P(x)=x^4-4x^3-x^2+20x-20=0[/tex]
By using synthetic division we can solve the polynomial:
2_| 1 -4 -1 20 -20
0 2 -4 -10 20
_____________________
1 -2 -5 10 |_0
Therefore x-2=0
x=2 is a zero of P(x)
Now we can write the cubic equation as below:
[tex]x^3-2x^2-5x+10=0[/tex]
Again using synthetic division
2_| 1 -2 -5 10
0 2 0 -10
______________
1 0 -5 |_0
Therefore x-2=0
x=2 is also a zero of P(x).
Now we have [tex]x^2+0x-5=0[/tex]
[tex]x^2-5=0[/tex]
[tex]x^2=5[/tex]
[tex]x^=\pm\sqrt{5}[/tex] is a zero of P(x)
Therefore the zeros are 2,2,[tex]\pm\sqrt{5}[/tex]
