Lesson M971  Understanding Quadratic Equations  1
The general form of a second order equation is ax^{2}+ bx + c = 0.
We call it a second order equation because the highest exponent on x is 2. The
order of an equation is determined by the highest exponent on a variable in the
equation. We say a is not equal to 0, because if a = 0 the equation could
be simplified to bx + c = 0, which is first order. However, b and c
can equal zero.
We call x the variable, and we call a, b, and c
coefficients. The coefficients are constant (they don't change).
Example 1: What are the coefficients a, b, and c in the
trinomial 6x^{2} x  3 = 0?
a = 6
b = 1
c = 3
Notice that c is equal to 3 and not 3. This is because the general
form is ax^{2}+ bx +c = 0, so if there is a negative sign in front of
the coefficient it has to be accounted for. Also notice that when no number is
written, 1 is assumed.
Quite often we must do some work on a second order equation to put it in the
general form.
Example 2: Write the equation x + 5x^{2} 6 = 20x  x^{2}
in the general form.
x + 5x^{2} 6 = 20x  x^{2}
5x^{2}+ x^{2} x  20x  6 = 0
6x^{2}
21x  6 = 0
2x^{2} 7x  2 =
0
Divide both sides by the GCF of 3.
What are the values of a, b, and c in the following equations?
1. x^{2} 3x + 4 = 0

2. 3x^{2} 4x + 5 = 0

3.  x^{2} 3x = 0

4. 5x^{2}+ 2 = 0

5. 3x^{2}+ x + 1 = 0

6. 6x^{2}+ 10 = 0

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