Question

Which of the following represents the zeros of f(x) = x3 − 14x2 + 61x − 84?

Answer 1

@lyn

Answer 2

@LynFran

Answer 3

@LynFran

Answer 4

@welshfella

Answer 5

try some of the factors of 84
f(4) = 0

so (x -4) is a factor

Answer 6

ok

Answer 7

3 a factor?

Answer 8

now as -84 is the last term and x - 4 is a factor you could see if the factors of 21 could be zeros

try finding f(3) and f(7)

Answer 9

so7,4, and 3

Answer 10

yes 3 is a factor

Answer 11

3 is a zero i meant

Answer 12

yes, may u help on another?

Answer 13

well is f(7) = 0 ?

Answer 14

you need to check that f(3) and f(7) = 0

Answer 15

ok, is 3 a factor?

Answer 16

or -3

Answer 17

i checked f(3) it is = 0 so 3 is a zero

Answer 18

and i checked 7 and it is a zero

Answer 19

3 is not a factor (x -3) will be a factor

Answer 20

ok

Answer 21

may you help on a nother

Answer 22

f(7) also = 0

yes 4,3 and 7 are correct

Answer 23

Which of the following is a polynomial with roots 3, 5i, and −5i?

Answer 24

ok

Answer 25

if x = 3 then one factor will be (x - 3)
and the other 2 will be (x + 5i) and (x - 5i)

what do you get when you multiply x + 5i and x - 5i ?

Answer 26

x^2-25i

Answer 27

@welshfella

Answer 28

not quite
(x - 5i)(x + 5i) = x^2 + 5xi - 5xi -5i*5i
= x^2 - 25i^2
= x^2 - 25* -1
= x^2 + 25

remember that i^2 = -1

Answer 29

ahh ok then what?

Answer 30

so to get your polynomial you must multiply:-
( x - 3)(x^2 + 25)

Answer 31

then we multiply by (X-3) for the answer right?

Answer 32

yeah that right

Answer 33

@welshfella what is our final answer?

Answer 34

well do the multiplication
(x - 3)(x^2 + 25)
= x^3 + 25x

can you continue?

Answer 35

you need to multiply the second parenthesis by -3

Answer 36

ok

Answer 37

-3x^2-75

Answer 38

f(x) = x^3 − 3x^2 + 15x − 75 IS THAT THE ANSWER?

Answer 39

@welshfella

Answer 40

its 25x not 15x

Answer 41

sry i mistyped

Answer 42

thanks dude

Answer 43

yw