Question

solve the equation in the real number system

x^4 - x^3 +2x^2 -4x -8 =0

Answer 1

Step 1:

The equation is .

Rational Root Theorem, if a rational number in simplest form is a root of the

polynomial equation , then is a factor of and  is a factor if _.

Rational zeros method:

If  is a rational zero, then  is a factor of 8 and  is a factor of 1.

The possible values of are  .

The possible values for are .

So, .

Make a table for the synthetic division and test possible  zeros.

	1	-1	2	-4	-8
1	1	0	2	-2	-10
2	1	1	4	4	0

Observe the table, ,solution of equation is 2.

The remaining equation is .

Answer 2

Step 2:

If is a rational zero, then is a factor of 4 and is a factor of 1.

The possible values of are  .

The possible values of are  .

so,.

Make a table for the synthetic division and test possible  zeros.

	1	1	4	4
1	1	2	6	10
-1	1	0	4	0

Observe the table, , solution of equation is .

The remaining equation is .

If remaining equation is solved the solutions are in complex numbers.

Therefore , the solutions in real number system are .

Solution:

The solutions of equation in real number system are .