1. faktorisasi
2. kuadrat sempurna
3. rumus
1. x² + 3x - 4 = 0
2. x² + 4x = 21
Jawab:
Penjelasan dengan langkah-langkah:
1. x² + 3x - 4 = 0
a. Faktorisasi
x² + 3x - 4 = (x - 1) (x + 4) = 0
x - 1 = 0 ⇒ x₁ = 1
x + 4 = 0 ⇒ x₂ = -4
HP = {x₁, x₂}
HP = {1, -4}
b. x² + 3x - 4 = 0
x² + 3x + (9/4) - (9/4) - 4 = 0
x² + 3x + (9/4) = (9/4) + 4
(x + (3/2))² = 25/4
x + (3/2) = ±√(25/4)
x + (3/2) = ±(5/2)
x = -(3/2) ± (5/2)
x₁ = -(3/2) + (5/2) = 2/2 = 1
x₂ = -(3/2) - (5/2) = -8/2 = -4
HP = {1, -4}
c. x₁,₂ = (-b ± [tex]\sqrt{b^{2}-4ac }[/tex]) / 2a
x₁,₂ = (-3 ± [tex]\sqrt{3^{2}-4(1)(-4) }[/tex]) / 2(1)
x₁,₂ = (-3 ± [tex]\sqrt{9+16}[/tex]) / 2
x₁,₂ = (-3 ± [tex]\sqrt{25}[/tex]) / 2
x₁,₂ = (-3 ± 5)/2
x₁ = (-3 + 5)/2 = 2/2 = 1
x₂ = (-3 - 5)/2 = -8/2 = -4
HP = {1, -4}
2. x² + 4x - 21 = 0
a. Faktorisasi
x² + 4x - 21 = (x - 3) (x + 7) = 0
x - 3 = 0 ⇒ x₁ = 3
x + 7 = 0 ⇒ x₂ = -7
HP = {x₁, x₂}
HP = {3, -7}
b. x² + 4x - 21 = 0
x² + 4x + 4 - 4 - 21 = 0
x² + 4x + 4 = 21 + 4
(x + 2)² = 25
x + 2 = ±√25
x + 2 = ± 5
x = -2 ± 5
x₁ = -2 + 5 = 3
x₂ = -2 - 5 = -7
HP = {-7, 3}
c. x₁,₂ = (-b ± [tex]\sqrt{b^{2}-4ac }[/tex]) / 2a
x₁,₂ = (-4 ± [tex]\sqrt{4^{2}-4(1)(-21) }[/tex]) / 2(1)
x₁,₂ = (-4 ± [tex]\sqrt{16+84}[/tex]) / 2
x₁,₂ = (-4 ± [tex]\sqrt{100}[/tex]) / 2
x₁,₂ = (-4 ± 10)/2
x₁ = (-4 + 10)/2 =6/2 = 3
x₂ = (-4 - 10)/2 = -14/2 = -7
HP = {3, -7}
semoga bermanfaat.............................
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