Question

if f(x) is a cubic polynomial and given the value of f(0) = 10, f(1) = 20, and f(2) = 30. Determine the value of f(2) + f(-2) ?

Answer 1

f(x) = ax^3 + bx^2 + cx + d

Answer 2

according information above, i get equations :
d = 10 ... (1)
a + b + c = 10 ... (2)
6a + 4b + 2c = 20 ... (3)
i stuck how to get the value of a, b , and c

Answer 3

* 8a + 4b + 2c = 20

Answer 4

f(2) = 8a + 4b + 2c + 10
f(-2) = -8a + 4b - 2c + 10
------------------------ (+)
f(2) + f(-2) = 8b + 20

hmm... still we have b unknown

Answer 5

yeah, i agree that

Answer 6

oh, maybe we can take respectively for x = 2, and x = -2 into the 2 equations

Answer 7

Do you mean pluging 2 , -2 in ?

Answer 8

d = 10
a + b +c = 10
4a + 2b + c = 10

f(x) = ax^3 + bx^2 + cx + d
f(-x) = -ax^3 +bx^2 -cx + d

f(x) + f(-x) = 2bx^2 + 2d

f(x) + f(-x) = 2bx^2 + 20

Answer 9

yeah, but looks doesnt work :)
must be solve for b, first

Answer 10

Yeah, we can notice that from the equation f(x) + f(-x) as if we set x = 2
we will get f(2) + f(-2) = 8b + 20

Answer 11

@tanjung can you take a snapshot for the original problem?

Answer 12

the problem is in indonesian language... i just trying translate it in english and all information is like aobve

Answer 13

So you forgot the most important tip while translating...@tanjung
Send it, Loser66 is Indonesian guru. @Loser66

Answer 14

hahaha.... it is funniest thing I 've ever seen. But, just post it, we may use google translation to figure out.

Answer 15

really ? :)

Answer 16

Cross our fingers. :)

Answer 17

problem 10, @Loser66

Answer 18

@Loser66, Damn dude, he wasn't joking it's real indonesian.

Answer 19

yeah, im indonesian @TrojanPoem :)

Answer 20

Yes, it is. :) https://www.google.com/?gws_rd=ssl#q=google+translate

Answer 21

To me, it looks like he translated it properly.

Answer 22

Let\[p(x) = x(x-1)(x-2) + 10(x+1)\]It satisfies all the above conditions.

Answer 23

waw, how can you got fast.... is it a counter solution ?

Answer 24

Also it seems that the answer to your question is not unique.\[p(x) = 2x(x-1)(x-2) + 10(x+1)\]\[p(x) = 3x(x-1)(x-2) + 10(x+1)\]all satisfy your condition but return different results.

Answer 25

so, the answer is many possible right ?

Answer 26

Yes, of course.

Answer 27

hey can u guys help me with a question sorry to intrude but this is urgent

Answer 28

is that ok

Answer 29

If you're given any more information, then we can work on the problem.

Answer 30

oh, ok i got it... thank you very much @ParthKohli

Answer 31

but what should i do while the question is instruct to me write the answer with the number 0 - 999 ? :)

Answer 32

To me, I have it in the form ax^3 +bx^2 + cx +d with b <0
Since, from above, we have a = -b /3
If b >0, then a <0 but the end of the cubic is positive infinitive, hence a must be >0, that gives us b <0,
if b =0, a =0, we don't have cubic.
Hence for b <0, let test b =-1, we have \(\dfrac{1}{3}x^3 -x^2 +\dfrac{32}{3}x +10\) satisfies the condition.
if b =-2, then \(\dfrac{2}{3}x^3 -2x^2+\dfrac{34}{3}x +10 \) satisfies the condition also.
Hence we have infinite many solution for it. To your grade, I think you just pick one of them, like the first one. and calculate f(-2) = -8, then f(2) + f(-2) = 30 -8 =22

Answer 33

k