Question

Solve each polynomial, show all values of x.x^4-3x^2-4=0

Answer 1

we have the polynomial

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

In this problem

we know that the value of x=2 is a zero of the polynomial

because

(2)^4-3(2)^2-4=0

therefore

To find out the other values of x

Divide'

x^4-3x^2-4 : (x-2)

x^3+2x^2+x+2

-x^4+2x^3

-----------------

2x^3-3x^2-4

-2x^3+4x^2

------------------

x^2-4

-x^2+2x

--------------

2x-4

-2x+4

-------------

0

therefore

x^4-3x^2-4=(x-2)( x^3+2x^2+x+2)

Solve the cubic equation

x^3+2x^2+x+2=0

The value of x=-2 is a zero of the cubic function

because

(-2)^3+2(-2)^2+(-2)+2=0

therefore

Divide

x^3+2x^2+x+2 : (x+2)

x^2+1

-x^3-2x^2

----------------------

x+2

-x-2

-------------

0

therefore

x^4-3x^2-4 =(x-2)(x+2)( x^2+1)

Solve the quadratic equation

x^2+1=0

`\begin{gathered} x^2=-1 \\ x=\pm\sqrt[]{-1} \\ x=\pm i \end{gathered}`

therefore

the answer is

the values of x are

x=2

x=-2

x=i

x=-i