jika a dan b adalah akar persamaan kuadrat 3x² + 5x + 1 =0 maka persamaan kuadrat baru akar akarnya (a-1) dan (b-1) adalah

a dan b akar pers [tex]3 x^{2} + 5 x^{1} +1 [/tex]

[tex] (x - a)(x-b) = 3x^{2} + 5x +1
  x^{2} - (a + b)x + ab = 3 x^{2} + 5x +1 [/tex]

-(a + b)x = 5x
 a + b = -5

ab = 1

[tex](a - 1)(b - 1) = ab - b -a + 1 = ab -(a+ b) + 1 = 1 + 5 + 1 = 7

pers barunya
[x - (a - 1)][x - (b -1)] = x^{2} - (b - 1)x - (a -1)x + (a -1) (b -1) x^{2} - [(a + b) - 2]x + [ab - (a + b) + 1] = x^{2} + 7x + 7