Odpowiedź:
[tex]f(0) = c = 0 \\ f(1) = a + b + 0 = 1 \\ f(2) = 4a + 2b + 0 = 3[/tex]
z układu równań:
[tex]a = b = \frac{1}{2} \\ c = 0[/tex]
więc
[tex]f(x) = \frac{1}{2} {x}^{2} + \frac{1}{2} x = \frac{1}{2} x(x + 1)[/tex]
[tex]( \frac{1}{2} x(x + 1)) {}^{2} = \frac{1}{4} {x}^{2} ( {x}^{2} + 2x + 1)[/tex]
[tex] \frac{1}{4} {x}^{2} {(x + 1)}^{2} = 0[/tex]
[tex]x = 0 \\ x = - 1[/tex]
