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Examples of Quadratic Equations
Quadratic Equations
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 ± √(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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Post by 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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NOTo share this example, copy and paste this code into your website, blog or forum:
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