Question

Find a rational zero of the polynomial function and use it to find all the zeros of the function.
f(x) = x^4 + 3x^3 - 5x^2 - 9x - 2

Answer 1

are u familiar with rational root theoreom?

Answer 2

yeah I think it is -1,2,-2
but my choices have {1,-2,-2 + sqrt3, -2-sqrt3} this is just an example there is four of them
so that confused me

Answer 3

a. {1,-2,-2 + sqrt3, -2-sqrt3}
b. {-1,-2,-2 + sqrt5, -2-sqrt5}
c. {-1,3,-2 + sqrt5, -2-sqrt5}
d. {-1,2,-2 + sqrt3, -2-sqrt3}

Answer 4

-1 , 2 is only rational roots

Answer 5

d is right

Answer 6

or so after that I have to find zero

Answer 7

u must factorise after that to find irrational zeros

Answer 8

okay thanks

Answer 9

i know that x=-1 is a root so i can factor out (x+1) like this
\( x^4 + 3x^3 - 5x^2 - 9x - 2=x^4+x^3+2x^3+2x^2-7x^2-7x-2x-2\\=x^3(x+1)+2x^2(x+1)-7x(x+1)-2(x+1)=(x+1)(x^3+2x^2-7x-2) \)

Answer 10

x=2 is a root also so u try to factor out x-2 from degree 3 polynomial , finally u will have a quadratic

Answer 11

so you just place 2 where 1 is right