If 2 4 0b ac− = - Repeated real solution. If 2 4 0b ac− > - Two real unequal solns. Quadratic Formula Solve 2 0ax bx c+ + =, 0a ≠ ( )( )2 2n n n n n nx a x a x a− = − + If n is odd then, © 2005 Paul Dawkinsīasic Properties & Facts Arithmetic OperationsĪ b a c b c a c b ca ba b c ac bcc ca ba b c ac bcc cĭistance Formula If ( )1 1 1,P x y= and ( )2 2 2,P x y= are two points the distance between them is © 2005 Paul Dawkins Algebra Cheat Sheet Basic Properties & Facts Arithmetic Operations (, 0 b ab ab ac ab c a c c a a a ac b b c bc b c a c ad bc a c ad bc b d bd b d bd a b b a a b a b c d d c c c c a ab ac ad b b c a c a bc d = - = - = - = - = ≠ = Exponent Properties ( ( ( ( 1 1 0 1 1, 0 1 1 n m m m n n m n m n m m m n m n nm n n n n n n n n n n n n n n n n a aa a a a a a a a a a a ab ab b b a a a a a b b a a a b a a - = ≠ = Properties of Radicals 1, if is odd, if is even n n n n n n mn nm n n n n n n a a ab a b a a a a b b a a n a a n = Properties of Inequalities If then and If and 0 then and If and 0 then and a b a c b c a c b c a b a b c ac bc c c a b a b c ac bc c c > Properties of Absolute Value if 0 if 0 a a a a a ≥ = - < 0 Triangle Inequality a a a a a ab ab b b a b a b ≥ - = ≤ Distance Formula If ( 1 1 1, P x y = and ( 2 2 2, P x y = are two points the distance between them is ( ( ( 2 2 1 2 2 1 2 1, d PP x x y y = - Complex Numbers ( ( ( ( ( ( ( ( ( ( ( ( ( ( 2 2 2 2 2 2 1 1, 0 Complex Modulus Complex Conjugate i i a i a a a bi c di a c b di a bi c di a c b di a bi c di ac bd ad bc i a bi a bi a b a bi a b a bi a bi a bi a bi a bi = - =- = ≥ = - = - = - = - =įor a complete set of online Algebra notes visit. For a complete set of online Algebra notes visit.
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