Question

Determine the zeros of f(x) = x3 + 7x2 + 10x − 6

Answer 1

Im lost :(

Answer 2

familiar with rational root theorem ?

Answer 3

I think so

Answer 4

good, what does it say ?

Answer 5

A theorem that provides a complete list of possible rational roots of the polynomial equation

Answer 6

Would it look like this give me a min

Answer 7

f(x) = 1x*3 + 7x*2 + 10x - 6
Factors of P = plus minus 1 , plus minus 2 and plus minus 3 and 6
Factors of Q = plus minus 1
P/Q = plusminus 1/1

Answer 8

thats right ! so the possible rational zeroes are : \[\large \pm 1 , ~\pm2, ~\pm 3, ~\pm 6\]

Answer 9

Solution would be 0 = x^3 + 7x^2 + 10x - 6
is x= 0.45 and x =-4.45

Answer 10

plugin x = 1 in the function,
do you get 0 ?

Answer 11

Yes

Answer 12

So there's a total of 3 zeros
Positive are 1 and 1
Negative is 2 and 0
And complez is 0 and 2

Answer 13

Am i correct ?

Answer 14

f(x) = x^3 + 7x^2 + 10x - 6

f(1) = 1^3 + 7(1)^2 + 10(1) - 6
= 1 + 7 + 10 - 6
= 12

which is NOT 0, so 1 is NOT a zero

Answer 15

lets try if -1 is a zero :

f(x) = x^3 + 7x^2 + 10x - 6

f(-1) = (-1)^3 + 7(-1)^2 + 10(-1) - 6
= -1 + 7 - 10 - 6
= -10

which is NOT 0, so -1 is NOT a zero

Answer 16

similalry can you test +-2 and +-3 also ?

Answer 17

Ok

Answer 18

So 2 / 1 7 10 -6
You would get
1 , 9 , 28 ,50

Answer 19

Yea

Answer 20

Then 3 is
3 / 1 , 7 , 10 , -6
Answers would be
1 , 10 , 40 , 114 am i correct

Answer 21

Oh nice, you're using synthetic division is it ?

Answer 22

try -3 also

Answer 23

Yes

Answer 24

-3 / 1, 7, 10, -6

Answer 25

1 , 10 , 40 ,114

Answer 26

thats for +3 right ?

Answer 27

what do you get for -3 ?

Answer 28

-3 / 1, 7, 10, -6

1, 4, -2, 0

Answer 29

so looks like -3 is a zero ?

Answer 30

and the depressed quadratic would be : \[\large x^2 + 4x - 2\]

which you can solve using quadratic formula to find the remaining two zeroes

Answer 31

OH ok i got the answer THANK U SO MUCH UR A LIFESAVER :) !!!!!!