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Nilai  dan  dari persamaan  berturut-turut adalah ....

Pertanyaan

Nilai begin mathsize 14px style x subscript 1 plus x subscript 2 end style dan begin mathsize 14px style x subscript 1 times x subscript 2 end style dari persamaan begin mathsize 14px style 2 straight x squared plus straight x equals 0 end style berturut-turut adalah ....

  1. begin mathsize 14px style negative 1 space dan space minus 1 half end style 

  2. size 14px minus size 14px 1 over size 14px 2 size 14px space size 14px dan size 14px space size 14px 0 

  3. size 14px 0 size 14px space size 14px dan size 14px space size 14px 1 over size 14px 2 

  4. size 14px 1 over size 14px 2 size 14px space size 14px dan size 14px space size 14px 1 

Pembahasan Soal:

Bentuk umum persamaan kuadrat:

undefined

Maka:

begin mathsize 14px style straight x subscript 1 plus straight x subscript 2 equals negative straight b over straight a end style dan begin mathsize 14px style straight x subscript 1 times straight x subscript 2 equals straight c over straight a end style.

Jika persamaan kuadaratnya adalah  begin mathsize 14px style 2 straight x squared plus straight x equals 0 end style,

Maka: begin mathsize 14px style straight a equals 2 comma space straight b equals 1 comma space straight c equals 0 end style sehingga diperoleh:

Error converting from MathML to accessible text. 

Jadi, Nilai begin mathsize 14px style x subscript 1 plus x subscript 2 end style dan begin mathsize 14px style x subscript 1 times x subscript 2 end style dari persamaan begin mathsize 14px style 2 straight x squared plus straight x equals 0 end style berturut-turut adalah begin mathsize 14px style negative 1 half space dan space 0 end style.

Oleh karena itu, Jawaban yang benar adalah B

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

R. RGFLLIMA

Terakhir diupdate 30 April 2021

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Pertanyaan yang serupa

Diketahui dan adalah akar-akar persamaan kuadrat berikut. Tentukan nilai , , , dan .

Pembahasan Soal:

Persamaan kuadrat size 14px x to the power of size 14px 2 size 14px plus size 14px 3 size 14px x size 14px minus size 14px 2 size 14px equals size 14px 0

 Diketahui: size 14px a size 14px equals size 14px 1 size 14px comma size 14px space size 14px b size 14px equals size 14px 3 size 14px comma size 14px space size 14px c size 14px equals size 14px minus size 14px 2

 size 14px alpha size 14px plus size 14px beta size 14px equals fraction numerator size 14px minus size 14px b over denominator size 14px a end fraction size 14px equals fraction numerator size 14px minus size 14px 3 over denominator size 14px 1 end fraction size 14px equals size 14px minus size 14px 3 

size 14px alpha size 14px. size 14px beta size 14px equals size 14px c over size 14px a size 14px equals fraction numerator size 14px minus size 14px left parenthesis size 14px minus size 14px 2 size 14px right parenthesis over denominator size 14px 1 end fraction size 14px equals size 14px 2

begin mathsize 14px style 1 over alpha plus 1 over beta equals fraction numerator beta plus alpha over denominator alpha. beta end fraction equals fraction numerator alpha plus beta over denominator alpha. beta end fraction equals negative 3 over 2 end style 

begin mathsize 14px style alpha squared plus beta squared equals left parenthesis alpha plus beta right parenthesis squared minus 2 left parenthesis alpha. beta right parenthesis equals left parenthesis negative 3 right parenthesis squared minus 2 left parenthesis 2 right parenthesis equals 9 plus 4 equals 13 end style 

 

Roboguru

Diketahui dan adalah akar-akar persamaan kuadrat berikut. Tentukan nilai , , , dan .

Pembahasan Soal:

Persamaan kuadrat undefined

Diketahui: begin mathsize 14px style a equals 1 comma space b equals 1 comma space c equals negative 1 end style

Penyelesaian:

size 14px alpha size 14px plus size 14px beta size 14px equals fraction numerator size 14px minus size 14px b over denominator size 14px a end fraction size 14px equals fraction numerator size 14px minus size 14px 1 over denominator size 14px 1 end fraction size 14px equals size 14px minus size 14px 1 

size 14px alpha size 14px. size 14px beta size 14px equals size 14px c over size 14px a size 14px equals fraction numerator size 14px minus size 14px 1 over denominator size 14px 1 end fraction size 14px equals size 14px minus size 14px 1 

size 14px 1 over size 14px alpha size 14px plus size 14px 1 over size 14px beta size 14px equals fraction numerator size 14px beta size 14px plus size 14px alpha over denominator size 14px alpha size 14px. size 14px beta end fraction size 14px equals fraction numerator size 14px alpha size 14px plus size 14px beta over denominator size 14px alpha size 14px. size 14px beta end fraction size 14px equals fraction numerator negative 1 over denominator negative 1 end fraction size 14px equals size 14px 1 

size 14px alpha to the power of size 14px 2 size 14px plus size 14px beta to the power of size 14px 2 size 14px equals size 14px left parenthesis size 14px alpha size 14px plus size 14px beta size 14px right parenthesis to the power of size 14px 2 size 14px minus size 14px 2 size 14px left parenthesis size 14px alpha size 14px. size 14px beta size 14px right parenthesis size 14px equals size 14px left parenthesis size 14px minus size 14px 1 size 14px right parenthesis to the power of size 14px 2 size 14px minus size 14px 2 size 14px left parenthesis size 14px minus size 14px 1 size 14px right parenthesis size 14px equals size 14px 1 size 14px plus size 14px 2 size 14px equals size 14px 3 

Roboguru

Diketahui dan adalah akar-akar persamaan kuadrat berikut. Tentukan nilai , , , dan .

Pembahasan Soal:

Persamaan kuadrat size 14px x to the power of size 14px 2 size 14px minus size 14px 3 size 14px x size 14px plus size 14px 1 size 14px equals size 14px 0 

Diketahui: begin mathsize 14px style a equals 1 comma space b equals negative 3 comma space c equals 1 end style  

Penyelesaian:

 begin mathsize 14px style alpha plus beta equals fraction numerator negative b over denominator a end fraction equals fraction numerator negative left parenthesis negative 3 right parenthesis over denominator 1 end fraction equals 3 end style 

begin mathsize 14px style alpha. beta equals c over a equals 1 over 1 equals 1 end style 

begin mathsize 14px style 1 over alpha plus 1 over beta equals fraction numerator beta plus alpha over denominator alpha. beta end fraction equals fraction numerator alpha plus beta over denominator alpha. beta end fraction equals 3 over 1 equals 3 end style 

begin mathsize 14px style alpha squared plus beta squared equals left parenthesis alpha plus beta right parenthesis squared minus 2 left parenthesis alpha. beta right parenthesis equals left parenthesis 3 right parenthesis squared minus 2.1 equals 9 minus 2 equals 7 end style 

Roboguru

Diketahui dan adalah akar-akar persamaan kuadrat berikut. Tentukan nilai , , , dan .

Pembahasan Soal:

Persamaan kuadrat size 14px x to the power of size 14px 2 size 14px minus size 14px 5 size 14px x size 14px minus size 14px 7 size 14px equals size 14px 0 

Diketahui: size 14px a size 14px equals size 14px 1 size 14px comma size 14px space size 14px b size 14px equals size 14px minus size 14px 5 size 14px comma size 14px space size 14px c size 14px equals size 14px minus size 14px 7 

 begin mathsize 14px style alpha plus beta equals fraction numerator negative b over denominator a end fraction equals fraction numerator negative left parenthesis negative 5 right parenthesis over denominator 1 end fraction equals 5 end style 

size 14px alpha size 14px. size 14px beta size 14px equals size 14px c over size 14px a size 14px equals fraction numerator size 14px minus size 14px 7 over denominator size 14px 1 end fraction size 14px equals size 14px minus size 14px 7 

begin mathsize 14px style 1 over alpha plus 1 over beta equals fraction numerator beta plus alpha over denominator alpha. beta end fraction equals fraction numerator alpha plus beta over denominator alpha. beta end fraction equals fraction numerator 5 over denominator negative 7 end fraction equals negative 5 over 7 end style 

size 14px alpha to the power of size 14px 2 size 14px plus size 14px beta to the power of size 14px 2 size 14px equals size 14px left parenthesis size 14px alpha size 14px plus size 14px beta size 14px right parenthesis to the power of size 14px 2 size 14px minus size 14px 2 size 14px left parenthesis size 14px alpha size 14px. size 14px beta size 14px right parenthesis size 14px equals size 14px left parenthesis size 14px 5 size 14px right parenthesis to the power of size 14px 2 size 14px minus size 14px 2 size 14px left parenthesis size 14px minus size 14px 7 size 14px right parenthesis size 14px equals size 14px 25 size 14px plus size 14px 14 size 14px equals size 14px 39 

 

Roboguru

Akar-akar persamaan kuadrat adalah • Nilai dari  adalah ...

Pembahasan Soal:

2 straight x squared space minus space 5 straight x space minus space 6 space equals space 0 space rightwards arrow space straight a space equals 2 semicolon space straight b space equals negative 5 semicolon space straight c equals 6  straight x subscript 1 plus straight x subscript 2 equals negative straight a over straight b equals 5 over 2  straight x subscript 1 space. space straight x subscript 2 equals straight c over straight a equals 6 over 2 equals 3  straight x subscript 1 over straight x subscript 2 plus straight x subscript 2 over straight x subscript 1 equals fraction numerator straight x subscript 1 squared plus straight x subscript 2 squared over denominator straight x subscript 1. straight x subscript 2 end subscript end fraction  equals fraction numerator open parentheses begin display style 5 over 3 end style close parentheses squared minus 2.3 over denominator 3 end fraction  equals fraction numerator begin display style 25 over 4 minus 6 over 1 end style over denominator 3 end fraction  equals fraction numerator 25 minus 24 over denominator 4 end fraction.1 third  equals 1 fourth.1 third equals 1 over 12

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