# Mastermind CAT Files -- CAT 2001 ALGEBRA

May 28th, 2015
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2. Ujakar and Keshav attempted to solve a quadratic equation. Ujakar made a mistake in writing down the constant term. He ended up with the roots (4,3). Keshav made a mistake in writing down the coefficient of x. He got the roots as (3,2).

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Algebra Cheat SheetBasic Properties & FactsArithmetic Operationsab ac ab c abc bca c ad bcb d bda b b ac d d cab acaExponent Propertiesa na m a nmn m b ab c ca ac b bca c ad bcb d bda b a bc c c ab c bcda n 1ma 0 1, a 0Properties of InequalitiesIf a b then a c b c and a c b ca bc ca bc cProperties of Absolute Valuea if a 0a if a 0a 0a aa ab ba b a b Triangle InequalityDistance FormulaIf P x1, y1 and P x2 , y2 are twopoints the distance between them is2 2 abnn b bnComplex Numbers1a n n n b a aProperties of Radicals1 nn 1m m1mi1 i 21a i a , a 0 a bi c di a c b d i a bi c di a c b d i a bi c di ac bd ad bc i a bi a bi a 2 b2

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