At a concession stand, three hot dog(s) and two hamburger(s) cost $8.00; two hot dog(s) and three hamburger(s) cost $8.25. F
1 answer:
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Answer: 3 zeroes.
Explanation:-
- The fundamental theorem of algebra states that any polynomial with degree m>0 and complex coefficients has atleast one complex root.
- Corollary of fundamental theorem states that for any polynomial with degree m>0 has exactly m solutions.
The given function is
Because it is a polynomial function with degree 3>0 , Therefore by corollary of fundamental theorem of algebra , it has 3 zeroes.
From the homogeneous part of the ODE, we can get two fundamental solutions. The characteristic equation is
which has roots at
. This admits the two fundamental solutions
The particular solution is easiest to obtain via variation of parameters. We're looking for a solution of the form
where
and
is the Wronskian of the fundamental solutions. We have
and so
Therefore the particular solution is
so that the general solution to the ODE is
which has roots at
The particular solution is easiest to obtain via variation of parameters. We're looking for a solution of the form
where
and
and so
Therefore the particular solution is
so that the general solution to the ODE is