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Examples of Quadratic Equations


Quadratic Equations

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

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 ± &#8730;(b2-4ac) > / 2a

Put in a, b and c:
x = < -6 ± &#8730;(62-4×5×1) > / (2×5)

Solve:
x = < -6 ± &#8730;(36-20) >/10
x = < -6 ± &#8730;(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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