Question

Please please please need help on 3 and 4 I’m really lost on them

Answer 1

1) Option c) is correct ie., 5 real and o non-real

2) Option b) is correct ie., (4,
`(1)/(2)`,
`(1)/(2)`, 2,2)

Explanation:

Given polynomial function is
`f(x)=x^5-3x^3-2`

To find zeros equate f(x) to zero ie.,
`f(x)=0`

`x^5-3x^3-2=0`

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

`x^3-x^2-2x+2=0`

| 1 -1 -2 2

1 | 0 1 0 2

|___________________

1 0 -2 0

x=1 is the zero

`x^2 -2 =0`

`x=\pm√(2)`

`x=√(2)` and

`x=√(-2)`

Option c) is correct ie., 5 real and o non-real

2) Given polynomial function is
`f(x)=(x-4)(2x-1)^2(x-2)^2`

To find zeros equate f(x) to zero ie.,
`f(x)=0`

`(x-4)(2x-1)^2(x-2)^2=0`

`(x-4)=0` (or)
`(2x-1)^2=0` or
`(x-2)^2=0`

Therefore x=4,
`x=(1)/(2)` of multiplicity of 2 and x=2 multiplicity of 2

Option b) is correct ie., (4,
`(1)/(2)`,
`(1)/(2)`, 2,2)