Akar – akar persanaan kuadrat x 2 + 4 x + K = 0 adalah x 1 dan x 2 . Jika x 12 – x 22 = -32, maka k

[tex]\displaystyle x_1^2-x_2^2=-32\\(x_1-x_2)(x_1+x_2)=-32\\\left(\pm\frac{\sqrt{D}}{a}\right)\left(-\frac{b}{a}\right)=-32\\\left(\pm\frac{\sqrt{b^2-4ac}}{a}\right)\left(-\frac{b}{a}\right)=-32\\\left(\pm\frac{\sqrt{(-4)^2-4(1)k}}{1}\right)\left(-\frac{4}{1}\right)=-32\\\pm\sqrt{16-4k}=8\\16-4k=64\\-4k=48\\\boxed{\boxed{k=-12}}[/tex]

Akar akar Persamaan Kuadrat
x² + 4x + k = 0
a= 1 , b = 4 , c = k
x₁ + x₂ - b/a= -4/1 = - 4
x₁ x₂ = c/a= k/1 = k
.
x₁² - x₂² = 32
(x₁+x₂)(x₁- x₂)  = 32
-4(x₁- x₂) = 32
(x₁- x₂) = - 8
(x₁-x₂)² = (-8)² = 64
(x₁+x₂)²- 4(x₁x₂) = 64
(-4)² - 4(k) = 64
16 -4k = 64
-4k = 48
k = -12