Question

MEDAL! Find all the zeros of the equation: x^4-6x^2-7x-6=0

Answer 1

I can't see any way to factor it ... Maybe it can be graphed?

Answer 2

\[x=\frac{ -\frac{ 1 }{ 2 }+\frac{ i }{ 2 }\pm \frac{ \sqrt{3}(1+1) }{ 2 } }{ 1 }-i\]

Answer 3

If there is a "nice" root, we can use the factors of the last term
+-6, +-3, +-2, +-1 divided by the factors of the first term (+-1)

I'd suggest using synthetic division since we have x^4
it can't be very large

Answer 4

It's easy to plug in +-1 to test
1: 1 - 6 -7 - 6 = -18
-1: 1 -6 +7 -6 = -4

What do we get if you plug +-2 in ?

Answer 5

I am so confused right now.... Where do I plug that in?

Answer 6

synthetic division with +-2 ?

Answer 7

is there a remainder ?

Answer 8

no.

Answer 9

x^3-2x^2-2x-3