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Question
Solve the following second degree equations in
1.
2.
In both cases, calculate the discriminant
then by setting
determine
such that
You can use the relation
a) The discriminant of the second degree equation
is equal to
The solutions of the second degree equation are:
et
b) The discriminant of the second degree equation
is equal to:
We look for a complex number
such that
Real numbers
and
must satisfy:
which is equivalent to:
which gives us, identifying real and imaginary parts:
(1)
(2)
We must also have
which gives:
(3)
Summing equations (1) and (3), we obtain:
Substracting equations (3) and (1), we obtain :
From equation (2), real numbers
and
have the same sign, hence the solutions for complex number
are:
or
We infer the solutions of the second degree equation:
