$x^2 + bx + c = 0$
$x_1 = 2$
$x_2 = 5$
$x_1 + x_2 = -b$
2 + 5 = −b
7 = −b
b = −7
$x_1x_2 = с$
2 * 5 = c
c = 10
$x^2 - 7x + 10 = 0$
Ответ: $x^2 - 7x + 10 = 0$

$x^2 + bx + c = 0$
$x_1 = -\frac{1}{3}$
$x_2 = 2$
$x_1 + x_2 = -b$
$-\frac{1}{3} + 2 = -b$
$-\frac{1}{3} + \frac{6}{3} = -b$
$\frac{5}{3} = -b$
$b = -\frac{5}{3}$
$x_1x_2 = с$
$-\frac{1}{3} * 2 = c$
$c = -\frac{2}{3}$
$x^2 - \frac{5}{3}x - \frac{2}{3} = 0$ |* 3
$3x^2 - 5x - 2 = 0$
Ответ: $3x^2 - 5x - 2 = 0$

$x^2 + bx + c = 0$
$x_1 = -0,2$
$x_2 = -10$
$x_1 + x_2 = -b$
−0,2 + (−10) = −b
−10,2 = −b
b = 10,2
$x_1x_2 = с$
−0,2 * (−10) = c
c = 2
$x^2 + 10,2x + 2 = 0$ |* 10
$10x^2 + 102x + 20 = 0$
Ответ: $10x^2 + 102x + 20 = 0$

$x^2 + bx + c = 0$
$x_1 = 2 - \sqrt{3}$
$x_2 = 2 + \sqrt{3}$
$x_1 + x_2 = -b$
$2 - \sqrt{3} + 2 + \sqrt{3} = -b$
$4 = -b$
$b = -4$
$x_1x_2 = с$
$(2 - \sqrt{3})(2 + \sqrt{3}) = c$
$c = 2^2 - (\sqrt{3})^2$
c = 4 − 3
c = 1
$x^2 - 4x + 1 = 0$
Ответ: $x^2 - 4x + 1 = 0$

$x^2 + bx + c = 0$
$x_1 = 0$
$x_2 = 6$
$x_1 + x_2 = -b$
0 + 6 = −b
6 = −b
b = −6
$x_1x_2 = с$
0 * 6 = c
c = 0
$x^2 - 6x + 0 = 0$
$x^2 - 6x = 0$
Ответ: $x^2 - 6x = 0$

$x^2 + bx + c = 0$
$x_1 = -\sqrt{7}$
$x_2 = \sqrt{7}$
$x_1 + x_2 = -b$
$-\sqrt{7} + \sqrt{7} = -b$
b = 0
$x_1x_2 = с$
$-\sqrt{7} * \sqrt{7} = c$
$c = -\sqrt{49}$
c = −7
$x^2 + 0x - 7 = 0$
$x^2 - 7 = 0$
Ответ: $x^2 - 7 = 0$