3rd degree polynomial (math)
I don't know whether it's a good idea asking you guys, since I probably don't know the right translations for the following math problem:
(am really a math noob, so idk what to do)
A 3rd degree polynomial has the same zeroing as function g(x)=x²-x-2.
It subtends the y - axis (ordinate) with P(0|2) and has the slope of -3.
What's the equation of the 3rd degree polynomial?
So far I know that the "base frame" for the polynomial is:
f(x)= ax³+ bx² + cx +d
and the first derivation is
f′(x)= 3ax² + 2bx +c
Also the zeroings of g(x) are Z1(-1|0) and Z2(2|0)
Idk what to do next cos i dont really understand a thing and what I just did there lol.
Also dunno whether you guys understand me (me and my translator lol).
But I would appreciate any helps!
You are on the right track.
There was be an easier way that I have forgotten however this will solve it.
Use the base frame and the derivative of the base frame.
First work out f(0)=2 and f'(0)=-3. (Ie substitute x for 0)
You will get two equations.
This gives d=2
And c=-3 from the derviative.
Now you do it for the two zeros. Ie f(-1)=0 and f(2)=0
This will give two equations with a,b, c and d. So you can the sustitue what c and d are into them (since you already know them) and then solve two simulataneous equations.
That is the method. You just need to do it now :)
Let me know if you are still stuck.
And your notation is interesting.
Amg thanks for your fast reply! And thanks, I also kind of understood what to do :
so I did this like you said:
f(2) = 0
8a+4b-3(2)+2 = 0
-a+b-1 = 0 | +1
-a+b = 1 |+a
Now I substitued b into 0=8a+4b-4 which will be:
Substitued a into 1+a:
The equation is:
Is this right? Because it's only 2. Degree polynomial
thanks in advance!
You just made an small in substitution. I have highlighted it out. Try again and see if that fixes it.
When you work out a and b again, see if f(0)=2 just to check.
ah right! I forgot that the double negative becomes +
so that'd be:
This time a into b
and then b back into a
the polynomial is:
I checked that with each of the conditions you specified it works.
Just make sure that f(-1)=0, f(2)=0, f(0)=2 (if you are in a hurry, check one of the first two as f(0) is a bad check in this case).
alright, thanks for that tip!
And thanks for your time and help! I appreciate it a lot! : D
You are welcome :).
Post again if you have any other questions. I should be able to do most final year highschool stuff. (If I have not forgotten, lol)
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