Answer :
Answer:
1) Option c) is correct ie., 5 real and o non-real
2) Option b) is correct ie., (4, [tex]\frac{1}{2}[/tex], [tex]\frac{1}{2}[/tex], 2,2)
Step-by-step explanation:
Given polynomial function is [tex]f(x)=x^5-3x^3-2[/tex]
To find zeros equate f(x) to zero ie., [tex]f(x)=0[/tex]
[tex]x^5-3x^3-2=0[/tex]
By synthetic division
| 1 0 -3 0 -2
-1 | 0 -1 1 2 2
|_________________
1 -1 -2 2 0
Therefore x=-1 is a zero
[tex]x^3-x^2-2x+2=0[/tex]
| 1 -1 -2 2
1 | 0 1 0 2
|___________________
1 0 -2 0
x=1 is the zero
[tex]x^2 -2 =0[/tex]
[tex]x=\pm\sqrt{2}[/tex]
[tex]x=\sqrt{2}[/tex] and
[tex]x=\sqrt{-2}[/tex]
Option c) is correct ie., 5 real and o non-real
2) Given polynomial function is [tex]f(x)=(x-4)(2x-1)^2(x-2)^2[/tex]
To find zeros equate f(x) to zero ie., [tex]f(x)=0[/tex]
[tex](x-4)(2x-1)^2(x-2)^2=0[/tex]
[tex](x-4)=0[/tex] (or) [tex](2x-1)^2=0[/tex] or [tex](x-2)^2=0[/tex]
Therefore x=4, [tex]x=\frac{1}{2}[/tex] of multiplicity of 2 and x=2 multiplicity of 2
Option b) is correct ie., (4, [tex]\frac{1}{2}[/tex], [tex]\frac{1}{2}[/tex], 2,2)