Question

Tentukan persamaan dari:
2x² + 5x + 3 = 0
[tex] \\ \\ \\ \\ \\ [/tex]
​

Answer 1

Jawab:
Hp = {- ³/₂, -1}

Penjelasan:
2x² + 5x + 3 = 0  {a ≠ 1}
ax² + bx + c = 0
a = 2, b = 5, c = 3

∵  a ≠ 1  ∴
p+q = b   pq = ac
p+q = 5   pq = 2(3)
p+q = 5   pq = 6
p = 2, q = 3

ax² + px + qx + c = 0   {a ≠ 1}  
2x² + 2x + 3x + 3 = 0
2x(x+1) + 3(x+1) = 0
(2x+3) (x+1) = 0
2x+3 = 0    x+1 = 0
2x = -3       x = -1
x = - ³/₂      x = -1
Hp = {- ³/₂, -1}

atau juga bisa begini
ax² + qx + px + c = 0   {a ≠ 1}  
2x² + 3x + 2x + 3 = 0
2x(x+³/₂) + 2(x+³/₂) = 0
(x+³/₂) (2x+2) = 0
x+³/₂ = 0    2x = -2
x = - ³/₂       x = -²/₂
x = - ³/₂      x = -1
Hp = {- ³/₂, -1}

(xcvi)