Question

determine the zeros of the polynomial function : f(x) = x^4 - 13x^2 +36

Answer 1

factor it set =0

Answer 2

=0

Answer 3

x^4 - 13x^2 + 36 = 0

Answer 4

then factor

Answer 5

http://www.purplemath.com/modules/factquad.htm

Answer 6

Set x^2 = t, and now you have a quadratic in t which you can solve by the factoring method. Once you have your t's, convert back to x.

Answer 7

ok just look at the problem this way

\[(x^2)^2 - 13(x^2) + 36 = 0\]

think of the x^2 as a single value

then factorise

\[(x^2 - 4)(x^2 - 9) = 0\]

now solve for x

Answer 8

(x-3)(X+3)(x-2)(x+2) ?

Answer 9

thats correct so you will have 4 solutions

Answer 10

cant you just write it like (x^2-4)(x^2-9)? < in factored form

Answer 11

It is not completely factored that way. If you look at each factor it still has an x^2 in it so you have to go further for the 4 solutions.

Answer 12

okay makes sense, thanks!

Answer 13

no as you need to find the zeros, this can only be done by solving, and this polynomial can be solved by factoring