Neka su
![a](/media/m/6/d/2/6d2832265560bb67cf117009608524f6.png)
,
![b](/media/m/e/e/c/eec0d7323095a1f2101fc1a74d069df6.png)
,
![c](/media/m/e/a/3/ea344283b6fa26e4a02989dd1fb52a51.png)
realni brojevi,
![a \not= 0](/media/m/8/d/9/8d9b8d58240436b4abf0347457eba186.png)
. Ako je
![x_1](/media/m/9/2/a/92aefd356eeab9982f45f21fb206a2ef.png)
jedno rješenje jednadžbe
![ax^2 + bx + c = 0](/media/m/e/c/4/ec49ee2c089f60eb4fcd7f7505dae13e.png)
i
![x_2](/media/m/a/a/1/aa16f4edacb7b534405242617406658f.png)
jedno rješenje jednadžbe
![-ax^2 + bx + c = 0\text{,}](/media/m/5/6/f/56fc1344461c21e7d2680b410e748acb.png)
dokažite da je tada jedno rješenje
![x_3](/media/m/4/3/a/43ae0683e5a02ed52f93b676eaa94cb4.png)
jednadžbe
![\frac{a}{2}x^2 + bx + c = 0\text{,}](/media/m/7/c/d/7cd1ae3ee06776f1038fe54a5f748f5a.png)
između
![x_1](/media/m/9/2/a/92aefd356eeab9982f45f21fb206a2ef.png)
i
![x_2](/media/m/a/a/1/aa16f4edacb7b534405242617406658f.png)
, tj.
![x_1 \leq x_3 \leq x_2](/media/m/f/b/3/fb312566d504401c7211c2d924a5e05e.png)
ili
![x_2 \leq x_3 \leq x_1](/media/m/a/4/5/a45987f25fd9157dc76603bf9846d97c.png)
.
%V0
Neka su $a$, $b$, $c$ realni brojevi, $a \not= 0$. Ako je $x_1$ jedno rješenje jednadžbe $$ax^2 + bx + c = 0$$ i $x_2$ jedno rješenje jednadžbe $$-ax^2 + bx + c = 0\text{,}$$ dokažite da je tada jedno rješenje $x_3$ jednadžbe $$\frac{a}{2}x^2 + bx + c = 0\text{,}$$ između $x_1$ i $x_2$, tj. $x_1 \leq x_3 \leq x_2$ ili $x_2 \leq x_3 \leq x_1$.