Question

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

Answer 1

Answer:

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

2) Option b) is correct ie., (4, $\frac{1}{2}$, $\frac{1}{2}$, 2,2)

Step-by-step 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

$x^2 -2 =0$

$x=\pm\sqrt{2}$

$x=\sqrt{2}$ and

$x=\sqrt{-2}$

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, $x=\frac{1}{2}$ of multiplicity of 2 and x=2 multiplicity of 2

Option b) is correct ie., (4, $\frac{1}{2}$, $\frac{1}{2}$, 2,2)