find of the real roots of the equation x4 - 5x2 + 4 =0​

Sagot :

x

=

±

2

,

±

1

EXPLANATION

Let

y

=

x

2

.

y

2

5

y

+

4

=

0

This is a nice and simple trinomial to factor.

(

y

4

)

(

y

1

)

=

0

y

=

4

or

y

=

1

We now reverse our substitution.

x

2

=

4

or

x

2

=

1

x

=

±

2

or

±

1

The graph of the function

f

(

x

)

=

x

4

5

x

2

+

4

confirms that there are zeroes at

x

=

±

2

and

±

1

.

graph{x^4 - 5x^2 + 4 [-10, 10, -5, 5]}

Answer:

Step-by-step explanation:

(x^2-1)(x^2-4)

x= +1, -1, +2, -2