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Quadratic Equations

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Quadratic Equation Notes O Level IGCSE Math Notes.
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   www.mathletics.com Curriculum ReadyQuadratic Equations Quadratic Equations  1 100% Quadratc Equatons Mathletics 100% © 3P Learning Quadratic Equations SERIES TOPIC K 7 If  x 2   =   16 , is  x   =   4  the only answer?Is it possible to nd soluons for  x  in ax 2   +   bx   +   c   =   0  based only on a , b  and c ?How many soluons does a quadrac equaon have?   QUADRATIC EQUATIONS A quadrac equaon is an equaon where the highest index is 2  (squared). These are a lile more complicated to solve than linear equaons, and may have no real soluons at all.  What do I know now that I didn't know before?    Answer these quesons,  before  working through the chapter.   I used to think: Answer these quesons,  afer   working through the chapter.   But now I think: If  x 2   =   16 , is  x   =   4  the only answer?Is it possible to nd soluons for  x  in ax 2   +   bx   +   c   =   0  based only on a , b  and c ?How many soluons does a quadrac equaon have?  2 100% Quadratc Equatons Mathletics 100% © 3P Learning Quadratic Equations SERIES TOPIC K 7 Basics Quadratic Equations If the highest index of the variable is 2 ( eg.  x 2 or  y 2 ) then the equaon is not linear, but is called a quadrac equaon . To nd the variable by itself on one side, the square root is used to change  x 2  to  x . But the  square root must be used on both sides.   Solve for  x   in the quadrac equaon  x x x x x x 2 16 342 16 16 34 1622218933 22222 2 !! + =+ - = -==== ^ h Each quadrac equaon can have one, two or no real soluons. The above example has two soluons (  x = -3 or    x = 3 ). Somemes the soluons will have to be le in surd form like this next example: Solve for  x   x x x x x 4 20 04 20555 2222 2 !! - ===== ^ h This equaon has the two possible soluons  x  5= or  x  5= Here is an example of a quadrac equaon with no real soluons: Solve for  x   in the quadrac equaon  x x x x x 3 8 43 8 8 4 83331244 2222 ! + =-+ - =- -= -=-= - This does not have any real soluons since no real number is the square root of a negave number. Subtract 16  from both sidesDivide both sides by 2 Because 3 9 2 =  and 3 9 2 - = ^ h Find the square root of both sides

contoh 2

Jul 23, 2017
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