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Akar-akar persamaan adalah

Akar-akar persamaan begin mathsize 14px style 1 half x squared minus x minus 3 equals 0 end style adalah undefined

  1. begin mathsize 14px style x subscript 1 comma 2 end subscript equals 1 plus-or-minus square root of 13 end style

  2. begin mathsize 14px style x subscript 1 comma 2 end subscript equals 1 plus-or-minus square root of 7 end style

  3. begin mathsize 14px style x subscript 1 comma 2 end subscript equals negative 1 plus-or-minus square root of 13 end style

  4. begin mathsize 14px style x subscript 1 comma 2 end subscript equals fraction numerator negative 1 plus-or-minus square root of 7 over denominator 2 end fraction end style

Jawaban:

Perhatikan bahwa persamaan kuadrat begin mathsize 14px style 1 half x squared minus x minus 3 equals 0 end style memiliki nilai begin mathsize 14px style a equals 1 half end stylesize 14px b size 14px equals size 14px minus size 14px 1, dan size 14px c size 14px equals size 14px minus size 14px 3.  Maka nilai diskriminan dari persamaan kuadrat tersebut adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row D equals cell b squared minus 4 a c end cell row blank equals cell open parentheses negative 1 close parentheses squared minus up diagonal strike 4 squared open parentheses 1 over up diagonal strike 2 to the power of 1 close parentheses open parentheses negative 3 close parentheses end cell row blank equals cell 1 plus 6 end cell row blank equals 7 end table end style

Dengan menggunakan rumus kuadratik

begin mathsize 14px style x subscript 1 comma 2 end subscript equals fraction numerator negative b plus-or-minus square root of D over denominator 2 a end fraction end style

diperoleh akar-akar

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 comma 2 end subscript end cell equals cell fraction numerator negative open parentheses negative 1 close parentheses plus-or-minus square root of 7 over denominator up diagonal strike 2 to the power of 1 open parentheses begin display style 1 over up diagonal strike 2 to the power of 1 end style close parentheses end fraction end cell row blank equals cell 1 plus-or-minus square root of 7 end cell end table end style

Jadi, jawaban yang tepat adalah B.

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