Tentukan persamaan kuadrat dengan akar akar sebagai berikut :
a. 3 dan 7
b. -1 dan 3
c. -4 dan 0
d. -3 dan -1/4
Materi : Bentuk dan Persamaan kuadrat
Soal Nomor 1
( x¹ = 3 , x² = 7 )
\___________/
( x - x¹ )( x - x² ) = 0
( x - 3 )( x - 7 ) = 0
x² - 10x + 21 = 0
Soal Nomor 2
( x¹ = -1 , x² = 3 )
\___________/
( x - x¹ )( x - x² ) = 0
( x + 1 )( x - 3 ) = 0
x² - 2x - 3 = 0
Soal Nomor 3
( x¹ = -4 , x² = 0 )
\____________/
( x - x¹ )( x - x² ) = 0
( x + 4 )( x ) = 0
x² + 4x = 0
Soal Nomor 4
( x¹ = -3 , x² = -¼ )
\____________/
( x - x¹ )( x - x² ) = 0
( x + 3 )( x + ¼ ) = 0
x² + 3x + ¼x + ¾ = 0
Semua dikalikan 4
4x² + 12x + x + 3 = 0
4x² + 13x + 3 = 0
Semoga bisa membantu
[tex] \boxed{ \colorbox{navy}{ \sf{ \color{lightblue}{ Answer\:by\: BLUEBRAXGEOMETRY}}}} [/tex]
Penjelasan dengan langkah-langkah:
Persamaan Kuadrat
a). x1 = 3 dan x2 = 7
(x - x1)(x - x2) = 0
(x - 3)(x - 7) = 0
x(x - 7) - 3(x - 7) = 0
x² - 7x - 3x + 21 = 0
x² - 10x + 21 = 0
.
b). x1 = -1 dan x2 = 3
(x - x1)(x - x2) = 0
(x + 1)(x - 3) = 0
x(x - 3) + 1(x - 3) = 0
x² - 3x + x - 3 = 0
x² - 2x - 3 = 0
.
c). x1 = -4 dan x2 = 0
(x - x1)(x - x2) = 0
(x + 4)(x - 0) = 0
x(x - 0) + 4(x - 0) = 0
x² - 0 + 4x - 0 = 0
x² + 4x = 0
.
d). x1 = -3 dan x2 = -1/4
(x - x1)(x - x2) = 0
(x +3)(x + 1/4) = 0
x(x + 1/4) + 3(x + 1/4) = 0
x² + 1/4x + 3x + 3/4 = 0 ---> kali kedua ruas sama dengan (4).
x².4 + 1/4x.4 + 3x.4 + 3/4.4 = 0
4x² + 4/4x + 12x + 12/4 = 0
4x² + x + 12x + 3 = 0
4x² + 13x + 3 = 0
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