Roots of quadratic equations of the form
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
The discriminant plays an important role in predicting the nature of the roots.
,the roots are imaginary and unequal
,the roots are real and unequal
,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:
part is ZERO, then,
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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