# Important General Laws and Formualae

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x = -b +- \/(b^2 -4.a.c) / 2a
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Discriminant inequality when quadratic inequality has 2 real roots
b^2 -4.a.c > 0
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Discriminant inequality of when quadratic inequality has 1 real root
b^2 -4.a.c = 0
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Discriminant inequality of when quadratic inequality has no real roots
b^2 -4.a.c < 0
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General rule - multiplying surds
\/(a) x \/(b) = \/(ab)
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General Rule - dividing surds
\/(a) / \/(b) = \/(a/b)
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General Rule - Rationalising the Denominator 1
a / \/(b) x \/(b) / \/(b) = a\/(b) / b
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General Rule - Rationalising the Denominator 2
a / b - \/(c) x b+\/(c) / b+\/(c) = ab+a\/(c) / b^2 - c
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a/b +/- c/d = ad+/-cb / bd
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General Rule - Multiplying fractions
a/b x c/d = ac/bd
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General Rule - Dividing fractions
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Factor Theorem
If F(a) = 0 then (x-a) is a factor
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Remainder Theorem 1
If we divide F(x) by (x-a) and we get F(a) = b where b does not equal 0, then b is a remainder
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Remainder Theorem 2
If we divide F(x) by (ax-b) then the remainder is F(b/a)
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## Other cards in this set

### Card 2

#### Front

Discriminant inequality when quadratic inequality has 2 real roots

b^2 -4.a.c > 0

### Card 3

#### Front

Discriminant inequality of when quadratic inequality has 1 real root

### Card 4

#### Front

Discriminant inequality of when quadratic inequality has no real roots

### Card 5

#### Front

General rule - multiplying surds