Persamaan kuadrat x^2 – ax + a + 1 = 0 mempunyai akar – akar x1 dan x2. Jika x1 – x2 = 1, maka a =

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Pertanyaan :


Persamaan kuadrat x^2 – ax + a + 1 = 0 mempunyai akar – akar x1 dan x2. Jika x1 – x2 = 1, maka a =

Jawaban :

X^2-ax+a+1 = 0
a = 1
b = -a
c = a+1

x1-x2 = 1
x1 = x2+1

x1+x2 = -b/a
x1+x2 = -(-a)/1
x2+1+x2 = a
2×2+1 = a

x1.x2 = c/a
x1.x2 = (a+1)/1
(x2+1).x2 = a+1
x2^2+x2 = 2×2+1+1
x2^2+x2 = 2×2+2
x2^2+x2-2×2-2 = 0
x2^2-x2-2 = 0
(x2-2)(x2+1) = 0
x2 = 2 atau x2 = -1

Jika x2 = 2:
a = 2×2+1
a = 2.2+1
a = 4+1
a = 5

Jika x2 = -1:
a = 2×2+1
a = 2.(-1)+1
a = -2+1
a = -1

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