SOLUTION: In the equation ax^2+bx+c=0, the value of b^2-4ac is called the _______ of the quadratic equation. What does this value tell you about the real roots of the equation.
Question 171214: In the equation ax^2+bx+c=0, the value of b^2-4ac is called the _______ of the quadratic equation. What does this value tell you about the real roots of the equation. Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website! is called the discriminant of the quadratic equation, . Note that this is the expression under the radical in the quadratic equation.
is the symbol for the discriminant, so
If then there is a single root to the quadratic with multiplicity of 2 and that root is . The term multiplicity of 2 arises from the fact that every quadratic can be represented as two factors: where and can be either complex or real numbers. In the case of , .
If then there are two distinct real number roots.
If then there is a conjugate pair of complex roots of the form where is the imaginary number defined by
