| Lesson M97-1 - Understanding Quadratic Equations - 1
The general form of a second order equation is ax2+ 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 6x2- 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 ax2+ 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 + 5x2- 6 = 20x - x2
in the general form.
-x + 5x2- 6 = 20x - x2
5x2+ x2- x - 20x - 6 = 0
6x2-
21x - 6 = 0
2x2- 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. x2- 3x + 4 = 0
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2. 3x2- 4x + 5 = 0
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3. - x2- 3x = 0
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4. 5x2+ 2 = 0
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5. 3x2+ x + 1 = 0
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6. -6x2+ 10 = 0
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