What are all the zeros of the equation x^4 -6x^2-7x-6=0

-2,3 and \frac{-1±i\sqrt{3} }{2}

Step-by-step explanation:

Given is an equation of power 4 in polynomial as

We have to find the zeroes of the funciton

By rational roots theorem since constant term = -6 and Leading coefficient =1

possible rational factors can be

±1,±2,±3,±6

By trial and error we try one by one.

So x=3 is zero and x-3 is factor

Try with -2

x=-2 is the zero

Now divide the given polynomial by (x+2)(x-3) to get quadratic form

Given polynomial =

Find the roots of quadratic by formula

x=

So roots are -2,3 and \frac{-1±i\sqrt{3} }{2}

ou would have 12 of each