Persamaan kuadrat yang akar-akarnya satu kurangnya dari dua kali akar-akar persamaan 4x^2-6x-1=0 adalah ?

4x^2 – 6x + 1 = 0
a = 4, b = – 6, c=1
X1 + x2 = – b/a = 6/4 = 3/2
X1.x2 = c/a = 1/4

Misal akar akar persamaan kuadrat baru adalah A dan B
A = 2×1 – 1
B = 2X2 – 1

A+B = 2×1 – 1 + 2×2 – 1
A+B = 2×1 + 2×2 – 2
A+B = 2(x1+x2) – 2
A+B = 2(3/2) – 2 = 3-2 = 1

A.B =(2×1-1)(2×2-1)
A.B= 2.×1.x2 – 2×1 – 2×2 + 1
A.B = 2.(x1.x2) – 2(x1+x2) + 1
A.B = 2(1/4) – 2(3/2) + 1
A.B = 1/2 – 3 + 1
A.B = 1/2 – 2 = 1/2 – 4/2 = – 3/2

Pk baru:
X^2 – (A+B) x + A.B = 0
X^2 – x – 3/2 = 0
2x^2 – 2x – 3 = 0