Somebody asked me if I can teach how to solve equations:
on
Where are any real numbers.
It really is easy!
Write the quadradic equation,
Since this is a quadradic equation.
Let , this is the discriminant.
There are three possibilities:
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1) : In this case the equation has two real solutions. Call them . Then the solution to is given by . Where are any real numbers.
2) . In this case the equation has one real solution. Call it . Then the solution to is given by .
3) . In this case the equation has two complex solutions. Since are real, the polynomial is a polynomial in real coefficients and hence the complex solutions come as complex conjuages. Thus let to the two solutions. Then is the solution to .