The Quadratic Formula returns 2, 1 or no values by adding and subtracting the square root of the discriminant (the value under the radical).

LAW OF TRICHTOMY

A quantity must be one of three things:

1. Less than zero (negative)
2. Equal to zero
3. Greater than zero (positive)

DISCRIMINANT

The value under the radical is the discriminant.  Since you have to find the square root for both equations, it is easier to do this first.

b^2 – 4ac

Using the Law of Trichtomy will tell you how many answers you have.

1.  None because you cannot find the square root of a negative number.

2.  Equal to zero one answer because you drop the plus or minus operations.

3.  Greater than zero, you have to find the square root.

:    If not a perfect square, factor out perfect squares and leave as a radical.

Given the form Ax^2 + Bx + c = 0  where

·        a is the coefficient of x^2

·        b is the coefficient of x

·        c is the constant

X1 = ( -b + sqrt ( b^2 – 4ac)) / 2a

X2 = ( -b sqrt ( b^2 – 4ac)) / 2a

PRACTICE

Ø      Practice the Quadratic Formula to solve p. 380, problems 23 – 28.

Ø      Practice the Quadratic Formula with any other functions you cannot factor from the worksheet or problems 5 – 22.  This helps you see how the formula works.

1.  Factor out any common monomial first to make the problem easier.

2.  List the values for a, b and c.

:    Remember the sign in front of the coefficient stays with the number.

3.  Find the value of the discriminant by substituting the values for a, b and c

4.  Using the value of the discriminant substitute the values for a, b and c into the 2 functions.

4.  Simplify the expressions