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Examples of Quadratic Equations

Quadratic Equations

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The name Quadratic comes from "quad" meaning square, because the variable gets squared (like x2).
**natttt***Posted on 2011-05-04 18:30:50*

**Quadratic Equation**looks like: ax2 + bx + c = 0

To find the solution you can use the special quadratic formula:

Some examples of

**solutions of quadratic equations**:

**x2 = 3x - 1**-> x2 - 3x + 1 = 0 -> a=1, b=-3, c=1

**2(w2 - 2w) = 5**-> 2w2 - 4w - 5 = 0 -> a=2, b=-4, c=-5

**z(z-1) = 3**-> z2 - z - 3 = 0 -> a=1, b=-1, c=-3

**5 + 1/x - 1/x2 = 0**-> 5x2 + x - 1 = 0 -> a=5, b=1, c=-1

**Example: Solve 5x˛ + 6x + 1 = 0**

Coefficients are:

a = 5, b = 6, c = 1

Quadratic Formula:

x = < -b ± √(b2-4ac) > / 2a

Put in a, b and c:

x = < -6 ± √(62-4×5×1) > / (2×5)

Solve:

x = < -6 ± √(36-20) >/10

x = < -6 ± √(16) >/10

x = ( -6 ± 4 )/10

x = -0.2 or -1

Check -0.2:

5×(-0.2)˛ + 6×(-0.2) + 1

= 5×(0.04) + 6×(-0.2) + 1

= 0.2 -1.2 + 1 = 0

Check -1:

5×(-1)˛ + 6×(-1) + 1

= 5×(1) + 6×(-1) + 1

= 5 - 6 + 1 = 0

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