Lesson Don't discriminate the DISCRIMINANT!!!!!

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//&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;ATTENTION &nbsp;(!)    &nbsp;&nbsp;&nbsp;&nbsp;ATTENTION &nbsp;(!)   &nbsp;&nbsp;&nbsp;&nbsp;ATTENTION &nbsp;(!)

//&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;This lesson is &nbsp;WRONG &nbsp;and its author is totally and absolutely &nbsp;UNQUALIFIED &nbsp;and &nbsp;IRRESPONSIBLE &nbsp;person,

//&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;who writes the discriminant incorrectly &nbsp;(!).  &nbsp;&nbsp;&nbsp;&nbsp;So, &nbsp;for your safety, &nbsp;ignore this lesson.

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//&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; - - - Wellwisher - - -

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Roots of quadratic equations of the form {{{ax^2+bx+c=0}}} has two types of roots:real, and imaginary.

Roots are obtained through factoring, completing th square, and the quadratic formula!

The quadratic formula has a discriminant. It is the {{{b^2+4*a*c}}} part.

The discriminant plays an important role in predicting the nature of the roots.

If {{{b^2+4*a*c<0}}},the roots are imaginary and unequal
~~~{{{b^2+4*a*c>0}}},the roots are real and unequal
~~~{{{b^2+4*a*c=0}}},the roots are real and equal.

Imaginary numbers are imaginary because it is the square root of a negative number. And, squaring a number means multiplying to itself. Thus, squaring any real number will produce a positive number and that negative numbers can not have a REAL square root.

The third condition CAN be easily PROVED!

Take note of the quadratic formula again:

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

and if {{{b^2-4*a*c}}} part is ZERO, then,

{{{x=(-b+-0)/(2*a)}}}

And we all know that adding or subtracting zero produces the same number.
Applying it, the roots are the same and equal.

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