Question

Find a third-degree polynomial function such that f(0) = -12 and whose zeros are 1, 2, and 3. Using complete sentences, explain how you found it

Answer 1

well if 1,2, 3 are the roots

(x-1)(x-2)(x-3) will be the third degree polynomial

Answer 2

but an additional condition given is that f(0)=-12

Answer 3

so we will have to make a slight change in our above polynomial ..any ideas?

Answer 4

note for (x-1)(x-2)(x-3) f(0)=-6

Answer 5

wait i dont understand

Answer 6

what do you not understand?

Answer 7

why did you do this (x-1)(x-2)(x-3) f(0)=-6 ?

Answer 8

do you understand how i got (x-1)(x-2)(x-3) ?

Answer 9

because the domains are 1 2 3?

Answer 10

because zeroes of function are 1 ,2,3

Answer 11

ok i got that part.

Answer 12

now wat?

Answer 13

now we could have reported this answer but the question insists on one more condition ie f(0)=-12

Answer 14

we currently have f(X)=(x-1)(x-2)(x-3)
f(0) =?

Answer 15

-12?

Answer 16

dont be lazy put x=0 and tell me what you get !

Answer 17

so it would be 0-1=-1? 0-2=-2? 0-3=-3?

Answer 18

try again ?

Answer 19

omg this is so hard!
do i plug in 1 for f(0)? like f(1)?

Answer 20

plug in 0 for f(0)

Answer 21

i dont understand! if i plug in 0 it would be f(0)

Answer 22

suppose f(X)=ax^3+bx^2+cx+d
so
f(0)=-12 --->put x=0 hten -12=d so d=-12
f(1)=0 as 1 is root
a+b+c+d=0
now f(2)=0
8a+4b+2c+d=0
f(3)=0
27a+9b+3c+d=0

solve the system of equation

Answer 23

i give up :/