Question

Find all zeros of f( x ) = x ^3 + 2 x ^2 − 9 x − 4

Answer 1

f( x ) = x ^3 + 2 x ^2 − 9 x − 4

p =-4

All factors of -4,

±1, ±2, ±4

q =1

All factors of 1,

±1

All possible ratios of p/q

±1, ±2, ±4

Find one that is a zero using synthetic division.

Let consider -4

-4|   1     2   -9   -4

        0   -4    8    4

       ------------------

        1    -2    -1   0

-4 is the zero of the function.

The depressed polynomial is x^2-2x-1

Find the roots of x^2-2x-1

Thus zeros are -4,1-√2 and 1+√2