How to find the median from a frequency table
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Answer:
Step-by-step explanation:
Our equations are
Let us understand the term Discriminant of a quadratic equation and its properties
Discriminant is denoted by D and its formula is
Where
a= the coefficient of the
b= the coefficient of
c = constant term
Properties of D: If D
i) D=0 , One real root
ii) D>0 , Two real roots
iii) D<0 , no real root
Hence in the given quadratic equations , we will find the values of D Discriminant and evaluate our answer accordingly .
Let us start with
Hence we have two real roots for this equation.
Hence we do not have any real root for this quadratic
Hence D>0 and thus we have two real roots for this equation.
Hence we have one real root to this quadratic equation.
The corresponding homogeneous ODE has characteristic equation with roots at
, thus admitting the characteristic solution
For the particular solution, assume one of the form
Substituting into the ODE gives
Then the general solution to this ODE is
Assume a solution of the form
Substituting into the ODE gives
so the solution is
Assume a solution of the form
Substituting into the ODE gives
so the solution is