Algebra II : Classification of roots using the discriminant
This is a free lesson from our course in Algebra II
 
   
In this section you'll explore with the help of several examples how to classify the roots using the discriminant from the quadratic formula. You may find it in the beginning to be elusive but walking through some examples with solution; and explanation by the instructor with the help of audio, video presentation in own handwriting; it may be simpler to understand.
In the quadratic equation ax2 + bx + c, the expression underneath the square root; sign i.e. b2 - 4ac is called the discriminant of the quadratic equation. It can be used to determine the condition for real, equal, or rational roots.A quadratic equation may have two (real) roots, one root or no roots. It does not have more than two roots, except in the situation if a = b = c = 0, where the expression exists for all values of x. (More text below video...)
<h2> Classification of roots using the discriminant - Watch video (Algebra II)</h2> <p> video, AlgebraII, practice questions, quizzes, subject, math help, complex numbers, classify the roots, determine real roots, determine equal roots, determine rational roots, imaginary roots, rational roots, irrational roots, example</p> <p> A quadratic equation may have two (real) roots, one root or no roots. It does not have more than two roots, except in the situation if a = b = c = 0, where the expression exists for all values of x.</p>
Other useful lessons:
Imaginary Unit
Plotting complex numbers on a 2D plane
Adding and Subtracting Complex Numbers
Multiply and Divide the complex numbers
Solving quadratic equation with imaginary roots
(Continued from above) The roots are given by
        x = {-b (b2 - 4ac)}/2a.
The conditions for the roots to be real, imaginary, rational, irrational, equal or unequal are as follows:
if b2 - 4ac < 0,  gives 2 conjugate imaginary  roots .
if b2 - 4ac = 0, gives 1  real, rational and equal root.
if b2 - 4ac > 0 and a perfect square, gives 2 real, rational and unequal root. If b2 - 4ac > 0 and not a perfect square, then it gives 1 real, irrational and unequal root.
For example, the quadratic equation y = x2 - 10x + 26 have two imaginary roots, since b2 - 4ac = -4 i.e. < 0.1
Note: When using the Quadratic Formula, make sure not to omit the ''sign, and be careful with the fraction line (it's under the initial b part, too).
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