Algebra 3 Solving Quadratic Equations Worksheet - Brunel University Page 7
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13Quadratic formula
2
ax
+ bx + c = 0
An arbitrary quadratic equation
can be solved by
formula
√
√
b ±
D
b ±
b
2
4ac
x
=
≡
1,2
2a
2a
Example
Solve, using the quadratic formula
2
x
+ 2x
35 = 0,
the following equation
Solution:
a = 1, b = 2, c =
35
Calculate the discriminant
√
D =
b
4ac
2
=
(4)
4 × 1 × ( 35)
2
√
√
=
4 + 140 =
144 = 12
2 ± 12
D > 0
=⇒
x
=
two zeros.
1,2
2
x
= 5, x
=
7
1
2
Note: you can solve this equation also by factorization
2
x
+ 2x
35 = (x
5)(x + 7) = 0, ⇒ x = 5, x =
7
7
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