Verify that the vector X is a solution of the given homogeneous system. X' = −1 1 25 1 −1 X; X = −1 5 e−6t/5 For X = −1 5 e−6t/5
, one has
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Given:
The polynomial function is
Yuri thinks that is a root of the given function.
To find:
Why cannot be a root?
Solution:
We have,
If is a root, then the value of the function at
is 0.
Putting in the given function, we get
Taking LCM, we get
Since the value of the function at is not equal to 0, therefore,
is not a root of the given function.