Question

find all zeros.

f(x)=x(5x-2)(x^2+1)



PLEASE HELP ME STEP BY STEP.

Answer 1

you can find the zeros of f by setting f(x)=0 and solving for x
you already have a factored expression for f

Recall if a*b=0 then a=0 or b=0 or both=0

so just solve your three equations you have there:
x=0 or 5x-2=0 or x^2+1=0

on of these equations is already solved

Answer 2

ok so i do this


5x-2=0
/ /
5 5

Answer 3

@freckles

Answer 4

what does that mean?

Answer 5

are you dividing both sides by 5?

Answer 6

\[\frac{5x-2}{5}=\frac{0}{5} \\ \frac{5x}{5}-\frac{2}{5}=0 \\ \frac{\cancel{5}x}{\cancel{5}}-\frac{2}{5}=0 \\ x-\frac{2}{5}=0\]
if so that is fine
what next step would you perform

Answer 7

2/5 = 0
0 0

x=2/5

Answer 8

right

Answer 9

well x=2/5
I think you meant you are just going to add 2/5 on both sides but yeah x=2/5 is right

Answer 10

now if you are to find the complex zeros you also need to solve x^2+1=0

Answer 11

ok

Answer 12

could you start me off

Answer 13

@freckles

Answer 14

subtract one on both sides

Answer 15

x^2=-1
now take square root of both sides
don't forget your plus or minus part

Answer 16

ok one sec

Answer 17

0^2?

Answer 18

the square root of -1 isn't 0
it is imaginary
people normally call sqrt(-1) , i

Answer 19

ok

Answer 20

i and-i

Answer 21

yes

Answer 22

so
-1=-i
(1)=i

Answer 23

x^2+1=0 (or the equivalent equation x^2=-1) gives the solutions x=-i or x=i
since (-i)^2=(-1)^2(i)^2=1(-1)=-1
and i^2=-1

Answer 24

ok thanks more?

Answer 25

more what?

Answer 26

more help please

Answer 27

you can post a question if you want

Answer 28

help me freckles