Question

Which part of the quadratic formula tells you whether the quadratic equation can be solved by factoring?

-b b2 - 4ac 2a

Use the part of the quadratic formula that you chose above and find its value given the following quadratic equation:

2x2 + 7x + 3 = 0

Answer 1

the second
7^2-4*2*3=...

Answer 2

The Discriminant
The quadratic formula can be used when the coefficients are any complex numbers. Now we want to focus our attention to equations with only real number coefficients. Notice the expression under the radical b2 – 4ac in the quadratic formula is called the discriminant. From this number we can determine the nature of the solutions of a quadratic equation.


Three possible cases:



1. b2 – 4ac = 0 Exactly one real number solution exists.


2. b2 – 4ac > 0 Two real number solutions exist.


3. b2 – 4ac < 0 Two complex solutions exist.

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