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Grafik fungsi kuadrat   selalu terletak di bawah sumbu . Nilai  yang memenuhi adalah ...

Pertanyaan

Grafik fungsi kuadrat space f left parenthesis x right parenthesis equals k x squared plus 8 x plus left parenthesis k space minus space 7 right parenthesis  selalu terletak di bawah sumbu X. Nilai k yang memenuhi adalah ... 

  1. k less than negative 1 

  2. k less than 0   

  3. negative 1 less than k less than 8 space space  

  4. negative 1 less than k less than 0 space space     

  5. 0 less than k less than 8 space space     

Pembahasan Soal:

syarat grafik kuadrat selalu di bawah sumbu X

k less than 0 D less than 0 

table attributes columnalign right center left columnspacing 0px end attributes row cell space f left parenthesis x right parenthesis end cell equals cell k x squared plus 8 x plus left parenthesis k space minus space 7 right parenthesis end cell row a equals cell k space space space space space b equals 8 space space space space space c equals k minus 7 end cell row D less than 0 row cell b squared minus 4 a c end cell less than 0 row cell 8 squared minus 4 k open parentheses k minus 7 close parentheses end cell less than 0 row cell 64 minus 4 k squared plus 28 k end cell less than 0 row cell 4 k squared minus 28 k minus 64 end cell greater than 0 row cell k subscript 1 comma 2 end subscript end cell equals cell fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction end cell row blank equals cell fraction numerator 28 plus-or-minus square root of 28 squared minus 4 times 4 times negative 64 end root over denominator 2 times 4 end fraction end cell row blank equals cell fraction numerator 28 plus-or-minus square root of 784 plus 1924 end root over denominator 8 end fraction end cell row blank equals cell fraction numerator 28 plus-or-minus square root of 1808 over denominator 8 end fraction end cell row blank equals cell fraction numerator 28 plus-or-minus 4 square root of 113 over denominator 8 end fraction end cell row cell k subscript 1 end cell equals cell fraction numerator 7 plus square root of 113 over denominator 2 end fraction space a t a u space k subscript 2 equals fraction numerator 7 minus square root of 113 over denominator 2 end fraction end cell row blank blank blank row cell k subscript 1 end cell equals cell 8 comma 8 space a t a u space k subscript 2 equals negative 1 comma 8 end cell row blank blank blank end table

open curly brackets k less than negative 1 comma 8 space a t a u space k greater than 8 comma 8 close curly brackets intersection open curly brackets k less than 0 close curly brackets equals open curly brackets k less than negative 1 comma 8 close curly brackets

Jadi, tidak ada jawaban yang tepat

 

 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Mei 2021

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