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Jika begin mathsize 14px style a end style dan begin mathsize 14px style b end style akar-akar persamaan kuadrat undefined dan begin mathsize 14px style b squared equals a plus 10 end style maka begin mathsize 14px style c squared plus c equals end style...

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Ingat konsep jumlah dan hasil kali akar dari begin mathsize 14px style A x squared plus B x plus C equals 0 end style:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 plus x subscript 2 end cell equals cell negative B over A end cell row cell x subscript 1 times x subscript 2 end cell equals cell C over A end cell end table end style  

Diketahui begin mathsize 14px style x squared minus left parenthesis a plus 3 right parenthesis x plus c equals 0 end style maka diperoleh begin mathsize 14px style A equals 1 comma space B equals negative left parenthesis a plus 3 right parenthesis comma space C equals c end style.

sehingga jika begin mathsize 14px style a end style dan begin mathsize 14px style b end style akar-akar persamaan kuadrat undefined maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 plus x subscript 2 end cell equals cell negative B over A end cell row cell a plus b end cell equals cell negative fraction numerator negative left parenthesis a plus 3 right parenthesis over denominator 1 end fraction end cell row cell a plus b end cell equals cell a plus 3 end cell row b equals 3 end table end style 

Karena begin mathsize 14px style b squared equals a plus 10 end style sehingga diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank b end table squared table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank a end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 10 end table 3 squared table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank a end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 10 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 9 end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank a end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 10 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank a end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 1 end table end style 

Karena begin mathsize 14px style b equals 3 comma space a equals negative 1 end style maka 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 times x subscript 2 end cell equals cell C over A end cell row cell a times b end cell equals cell c over 1 end cell row cell left parenthesis negative 1 right parenthesis times 3 end cell equals c row c equals cell negative 3 end cell end table end style 

Jadi

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell c squared plus c end cell equals cell left parenthesis negative 3 right parenthesis squared plus left parenthesis negative 3 right parenthesis end cell row blank equals cell 9 minus 3 end cell row blank equals 6 end table end style.

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