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4. Equació 2n grau

bold italic a bold italic x to the power of bold 2 bold plus bold italic b bold italic x bold plus bold italic c bold equals bold 0 space space space space space space space space space space left parenthesis a not equal to 0 right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space space space space bold italic x bold equals fraction numerator bold minus bold b bold plus-or-minus square root of bold b to the power of bold 2 bold minus bold 4 bold ac end root over denominator bold 2 bold a end fraction

                               

Exemple 1

bold 2 bold italic x to the power of bold 2 bold plus bold 3 bold italic x bold minus bold 2 bold equals bold 0 space space space space space space space space space space x equals fraction numerator negative 3 plus-or-minus square root of left parenthesis negative 3 right parenthesis squared minus 4 times 2 times left parenthesis negative 2 right parenthesis end root over denominator 2 times 2 end fraction equals fraction numerator negative 3 plus-or-minus square root of 9 plus 16 end root over denominator 4 end fraction equals fraction numerator negative 3 plus-or-minus square root of 25 over denominator 4 end fraction equals fraction numerator negative 3 plus-or-minus 5 over denominator 4 end fraction equals open curly brackets table attributes columnalign left end attributes row cell fraction numerator negative 3 plus 5 over denominator 4 end fraction equals 2 over 4 equals bold 1 over bold 2 end cell row cell fraction numerator negative 3 minus 5 over denominator 4 end fraction equals fraction numerator negative 8 over denominator 4 end fraction equals bold minus bold 2 end cell end table close

Exemple 2

bold 2 bold italic x to the power of bold 2 bold minus bold 3 bold italic x bold minus bold 2 bold equals bold 0 bold space bold space bold space bold space bold space space space space space space x equals fraction numerator negative left parenthesis negative 3 right parenthesis plus-or-minus square root of left parenthesis negative 3 right parenthesis squared minus 4 times 2 times left parenthesis negative 2 right parenthesis end root over denominator 2 times 2 end fraction equals fraction numerator 3 plus-or-minus square root of 9 plus 16 end root over denominator 4 end fraction equals fraction numerator 3 plus-or-minus square root of 25 over denominator 4 end fraction equals fraction numerator 3 plus-or-minus 5 over denominator 4 end fraction equals open curly brackets table attributes columnalign left end attributes row cell fraction numerator 3 plus 5 over denominator 4 end fraction equals 8 over 4 equals bold 2 end cell row cell fraction numerator 3 minus 5 over denominator 4 end fraction equals fraction numerator negative 2 over denominator 4 end fraction equals bold minus bold 1 over bold 2 end cell end table close

Exemple 3

bold italic x to the power of bold 2 bold minus bold 5 bold italic x bold plus bold 6 bold equals bold 0 space space space space space space space space space space x equals fraction numerator negative left parenthesis negative 5 right parenthesis plus-or-minus square root of left parenthesis negative 5 right parenthesis squared minus 4 times 1 times 6 end root over denominator 2 times 1 end fraction equals fraction numerator 5 plus-or-minus square root of 25 minus 24 end root over denominator 2 end fraction equals fraction numerator 5 plus-or-minus square root of 1 over denominator 2 end fraction equals fraction numerator 5 plus-or-minus 1 over denominator 2 end fraction equals open curly brackets table attributes columnalign left end attributes row cell fraction numerator 5 plus 1 over denominator 2 end fraction equals 6 over 2 equals bold 3 end cell row cell fraction numerator 5 minus 1 over denominator 2 end fraction equals 4 over 2 equals bold minus bold 2 end cell end table close

Exemple 4

bold italic x to the power of bold 2 bold minus bold 5 bold italic x bold plus bold 7 bold equals bold 0 space space space space space space space space space space x equals fraction numerator negative left parenthesis negative 5 right parenthesis plus-or-minus square root of left parenthesis negative 5 right parenthesis squared minus 4 times 1 times 7 end root over denominator 2 times 1 end fraction equals fraction numerator 5 plus-or-minus square root of 25 minus 28 end root over denominator 2 end fraction equals fraction numerator 5 plus-or-minus square root of negative 3 end root over denominator 2 end fraction space space space space bold italic N bold italic o bold space bold italic t bold italic é bold space bold italic s bold italic o bold italic l bold italic u bold italic c bold italic i bold italic ó

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