Question

Diket akar akar persamaan kuadrat 2X^2+5X+6=0 adalah X1 dan X2. persamaan kuadrat yg akarnya 1/X1-5 dan 1/X2-5 adalah...

Answer 1

2x² + 5x + 6 = 0
x₁ + x₂ = - 5/2
x₁x₂ = 6/2 = 3

Persamaan kuadrat baru:
x² - (1/x₁ + 1/x₂ - 10)x + (1/x₁x₂ - 5(1/x₁ + 1/x₂) + 25) = 0
x² - ((x₁ + x₂)/x₁x₂ - 10)x + (1/x₁x₂ - 5((x₁ + x₂)/x₁x₂) + 25) = 0
x² - ((-5/2)/3 - 10)x + (1/3 - 5((-5/2)/3) + 25) = 0
x² - (-5/6 - 10)x + (1/3 + 25/6 + 25) = 0
x² + (65/6)x + 177/6 = 0
6x² + 65x + 177 = 0