Quadratic Equation
A quadratic equation is one where one of the terms is squared. A quadratic equation is of the form:
aX2 + bX + c = 0, where a, b, and c are integers.
Here are some quadratic equations:
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X2 + 4X - 45 = 0 | In this equation, X = 5 because 52 + (4)(5) - 45 = 0.
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Constants:
a = 1, b = 4, c = -45
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| 2 X2 -18 = 0 | In this equation, X = 3 because 2 X 9 - 18 = 0
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Constants:
a = 2, b = 0, c = -18
Note: b = 0 because there is no X term
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X2 + 4X = 45 | This is the same equation as the first one, except that 45 appears after the equal sign. To get it into a standard form,subtract 45 from both sides of the equation to put it in the form X2 + 4X - 45 = 0 |
Constants:
a = 1, b = 4, c = -45
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Sometimes it's not so easy to find X. For these cases you need a formula to compute X given the constants (a, b and c) in the equation.
Here is that formula:
x = -b ± √
b 2 -
4 a c
2a
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The ± ("plus or minus") means that there are 2 solutions for X, one using the positive (+) value of the square root and one the negative (-) value.
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When you think about it, X2 = 25 has another solution: X = - 5 because - 5 x - 5 = + 25 also.
If you apply this formula to our first equation: X2 + 4X - 45 = 0, (a = 1, b = 4 and c = - 45) you get:
X = - 4 ± √
4 2 -
(4) (1) (-45) So:
2
X = - 4 ± √16 +180 =
2
X = - 4 ± 14 =
2
X = - 2 ± 7 = + 5 or - 9: A value of - 9 also works because (-9)2 -36 -45 = 0 also!
OK, here's a problem for you! Solve for X:
2X2 - 2X - 24 = 0 a = ____ b = _____ and c = _____
X = ______
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