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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. f(0)=a0^3+b0^2+c0+d=2 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 0=8a+4b-4 f(-1)=0 -a+b-3+2=0 -a+b-1 = 0 | +1 -a+b = 1 |+a b= 1+a Now I substitued b into 0=8a+4b-4 which will be: 8a+4(1+a)-4 0=8a+4+4a-4 0=12a|:12 a=0 Substitued a into 1+a: b=1+0 =1 The equation is: f(x)=x²+3x+2 Is this right? Because it's only 2. Degree polynomial thanks in advance! |

Quote:
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 +
f(-1)=-a+(-1)^2*b-(-1)3+2 so that'd be: 0=-a+b+5|+a a=b+5 This time a into b 0=8a+4b-4|+4 4=8(b+5)+4b 4=12b+40|-40 -36=12b|:12 b=-3 and then b back into a a=-3+5 a=2 the polynomial is: f(x)=2x³-3x²-3x+2 right? |

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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