Write the polynomial of the smallest degree with roots 4, -2, 1, and 2

Question

tamtoan · Answer

if a polynomial have roots a and b, you can write it as ...(x-a)(x-b) = 0 ...can you use this to write your polynomial with those roots?

anonymous · Answer

i suppose

tamtoan · Answer

can you let me know what your polynomial is ?

anonymous · Answer

4,-2,1 and 2

tamtoan · Answer

those are the roots :) , you have to write your polynomial ...in the form of $$a x ^{n} + b x^{n-1}+ ....+C    $$  <---  this last coordinate is a big constant C

lacypennelll · Answer

yummy dum ;3 nice name

anonymous · Answer

the smallest degree it can have is $4$ since there are four zeros....all you have to do is make binomials given the zeros...as such:$$x=4~~\implies~~(x-4)$$$$x=-2~~\implies~~(x+2)$$$$x=1~~\implies~~(x-1)$$$$x=2~~\implies~~(x-2)$$so now you just have to multiply those together:$$(x-4)(x+2)(x-1)(x-2)$$$$(x^2-2x-8)(x^2-3x+2)$$$$x^4-5x^3+20x-16$$
hope that helps @coolaidd ! :)

anonymous · Answer

lol, its got quite the history :)

lacypennelll · Answer

lol cool:D

lacypennelll · Answer

i shoudl have had a name like that >.<

lacypennelll · Answer

should*