Question

x²+2x-24=0
x²-9x+20=0
10n²-9n+2=0
21y²-2y-3=0

Answer 1

Задача 1 ([1, 2, -24])

$1 \cdot x^2 + 2 \cdot x + -24 = 0$

$D = b^2 - 4 \cdot a \cdot c = 2^2 - 4 \cdot 1 \cdot -24 = 100$

D > 0

$x_{1} = \frac{-b - \sqrt{D}}{2a} = \frac{-2 - \sqrt{100}}{2\cdot1} = \frac{-12.0}{2} = -6.0$

$x_{2} = \frac{-b + \sqrt{D}}{2a} = \frac{-2 + \sqrt{100}}{2\cdot1} = \frac{8.0}{2} = 4.0$

Ответ: [-6.0, 4.0]

Задача 2 ([1, -9, 20])

$1 \cdot x^2 + -9 \cdot x + 20 = 0$

$D = b^2 - 4 \cdot a \cdot c = -9^2 - 4 \cdot 1 \cdot 20 = 1$

D > 0

$x_{1} = \frac{-b - \sqrt{D}}{2a} = \frac{9 - \sqrt{1}}{2\cdot1} = \frac{8.0}{2} = 4.0$

$x_{2} = \frac{-b + \sqrt{D}}{2a} = \frac{9 + \sqrt{1}}{2\cdot1} = \frac{10.0}{2} = 5.0$

Ответ: [4.0, 5.0]

Задача 3 ([10, -9, 2])

$10 \cdot x^2 + -9 \cdot x + 2 = 0$

$D = b^2 - 4 \cdot a \cdot c = -9^2 - 4 \cdot 10 \cdot 2 = 1$

D > 0

$x_{1} = \frac{-b - \sqrt{D}}{2a} = \frac{9 - \sqrt{1}}{2\cdot10} = \frac{8.0}{20} = 0.4$

$x_{2} = \frac{-b + \sqrt{D}}{2a} = \frac{9 + \sqrt{1}}{2\cdot10} = \frac{10.0}{20} = 0.5$

Ответ: [0.4, 0.5]

Задача 4 ([21, -2, -3])

$21 \cdot x^2 + -2 \cdot x + -3 = 0$

$D = b^2 - 4 \cdot a \cdot c = -2^2 - 4 \cdot 21 \cdot -3 = 256$

D > 0

$x_{1} = \frac{-b - \sqrt{D}}{2a} = \frac{2 - \sqrt{256}}{2\cdot21} = \frac{-14.0}{42} = -0.3333333333333333$

$x_{2} = \frac{-b + \sqrt{D}}{2a} = \frac{2 + \sqrt{256}}{2\cdot21} = \frac{18.0}{42} = 0.42857142857142855$

Ответ: [-0.3333333333333333, 0.42857142857142855]