the quadratic formula. what does the quadratic formula do ? the quadratic formula allows you to find...
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The Quadratic Formula
a
acbbx
2
42
What does the Quadratic Formula Do ?
The Quadratic formula allows you to find the roots of a quadratic equation (if they exist) even if the quadratic equation does not factorize.
The formula states that for a quadratic equation of the
form : ax2 + bx + c = 0
The roots of the quadratic equation are given by :
a
acbbx
2
42
Example 1
Use the quadratic formula to solve the equation : x 2 + 5x + 6= 0
Solution:
Given: x 2 + 5x + 6= 0
Where a = 1 b = 5 c = 6
a
acbbx
2
42
12
)614(55 2
x
2
)24(255 x
2
15x
2
15
2
15
xorx
x = - 2 or x = - 3
These are the roots of the original equation.
and
then, substituting gives
Example 2
Use the quadratic formula to solve the equation: 8x 2 + 2x - 3= 0
Solution:
Given: 8x 2 + 2x - 3= 0
Where a = 8 b = 2 c = -3
a
acbbx
2
42
82
)384(22 2
x
16
)96(42 x
16
1002x
16
102
16
102
xorx
x = ½ or x = - ¾
These are the roots of the original equation..
and
then, substituting gives
Example 3
Use the quadratic formula to solve the equation: 8x 2 - 22x + 15= 0
Solution:
Given: 8x 2 - 22x + 15= 0
Where a = 8 b = -22 c = 15
a
acbbx
2
42
82
)1584()22()22( 2
x
16
)480(484(22 x
16
422x
16
222
16
222
xorx
x = 3/2 or x = 5/4 These are the roots of the original
equation.
and
then, substituting gives
Example 4
Use the quadratic formula to solve for x to 2 decimal places: 2x 2 +3x - 7= 0
Solution:
Given: 2x 2 + 3x – 7 = 0
Where a = 2 b = 3 c = - 7
a
acbbx
2
42
22
)724(33 2
x
4
)56(93 x
4
653x
4
06.83
4
06.83
xorx
x = 1.27 or x = - 2.77These are the roots of the original
equation.
and
then, substituting gives