Question

find all the root of the equation x9-x5+x4-1=0​

Answer 1

Answer:

Give equation, x

9

−x

5

+x

4

+x

2

+1=0, has two changes of signs. Hence there can be a maximum of 2 positive roots.

f(−x)=−x

9

+x

5

+x

4

+x

2

+1=0, which has one changes of signs. Hence the given equation has a maximum of 1 negative roots.

Now, as the equation is of 9

th

degree, it must have at least (9−2−1)=6 imaginary roots.