Question

1) 2x²+3x - 1 =0, D=3²-4.2.1; 2) 3x²-4x + 2 =0, D=(-4)²-4.3.2; 3) 0,5x²-5x+3=0, D=(-5)²-4·3-0,5 4) -6x²-5x-1=0, D=(-6)²-4·5·1?​

Answer 1

Задача 1 ([2, 3, -1])

$2 \cdot x^2 + 3 \cdot x - 1 = 0$

$D = b^2 - 4 \cdot a \cdot c = 3^2 - 4 \cdot 2 \cdot -1 = 17$

D > 0

$x_{1} = \frac{-b - \sqrt{D}}{2a} = \frac{-3 - \sqrt{17}}{2\cdot2} = \frac{-7.123105625617661}{4} = -1.7807764064044151$

$x_{2} = \frac{-b + \sqrt{D}}{2a} = \frac{-3 + \sqrt{17}}{2\cdot2} = \frac{1.1231056256176606}{4} = 0.28077640640441515$

Ответ: [-1.7807764064044151, 0.28077640640441515]

Задача 2 ([3, -4, 2])

$3 \cdot x^2 - 4 \cdot x + 2 = 0$

$D = b^2 - 4 \cdot a \cdot c = -4^2 - 4 \cdot 3 \cdot 2 = -8$

D < 0, значит действительных корней не существует, а комплексные корни такие:

$x_{1} = \frac{-b - \sqrt{D}i}{2a} = \frac{4 - \sqrt{-8}i}{2\cdot3} = 0 - 0.47140452079103173i$

$x_{2} = \frac{-b + \sqrt{D}i}{2a} = \frac{4 + \sqrt{-8}i}{2\cdot3} = 0 + 0.47140452079103173i$

Задача 3 ([0.5, -5, 3])

$0.5 \cdot x^2 - 5 \cdot x + 3 = 0$

$D = b^2 - 4 \cdot a \cdot c = -5^2 - 4 \cdot 0.5 \cdot 3 = 19.0$

D > 0

$x_{1} = \frac{-b - \sqrt{D}}{2a} = \frac{5 - \sqrt{19.0}}{2\cdot0.5} = \frac{0.641101056459326}{1.0} = 0.641101056459326$

$x_{2} = \frac{-b + \sqrt{D}}{2a} = \frac{5 + \sqrt{19.0}}{2\cdot0.5} = \frac{9.358898943540673}{1.0} = 9.358898943540673$

Ответ: [0.641101056459326, 9.358898943540673]

Задача 4 ([-6, -5, -1])

$-6 \cdot x^2 - 5 \cdot x - 1 = 0$

$D = b^2 - 4 \cdot a \cdot c = -5^2 - 4 \cdot -6 \cdot -1 = 1$

D > 0

$x_{1} = \frac{-b - \sqrt{D}}{2a} = \frac{5 - \sqrt{1}}{2\cdot-6} = \frac{4.0}{-12} = -0.3333333333333333$

$x_{2} = \frac{-b + \sqrt{D}}{2a} = \frac{5 + \sqrt{1}}{2\cdot-6} = \frac{6.0}{-12} = -0.5$

Ответ: [-0.3333333333333333, -0.5]

Answer 2

It looks like you're trying to calculate the discriminant (D) for different quadratic equations. The discriminant is used to determine the nature of the solutions (roots) of a quadratic equation. The formula for the discriminant is:

D = b² - 4ac

Where:

• a, b, and c are the coefficients of the quadratic equation in the form ax² + bx + c = 0.

Let's calculate the discriminant for each of the equations you've provided:

1. For the equation 2x² + 3x - 1 = 0: a = 2, b = 3, c = -1 D = (3)² - 4(2)(-1) D = 9 + 8 D = 17

2. For the equation 3x² - 4x + 2 = 0: a = 3, b = -4, c = 2 D = (-4)² - 4(3)(2) D = 16 - 24 D = -8

3. For the equation 0.5x² - 5x + 3 = 0: a = 0.5, b = -5, c = 3 D = (-5)² - 4(0.5)(3) D = 25 - 6 D = 19

4. For the equation -6x² - 5x - 1 = 0: a = -6, b = -5, c = -1 D = (-5)² - 4(-6)(-1) D = 25 - 24 D = 1

So, the discriminants for the four equations are:

1. D = 17
2. D = -8
3. D = 19
4. D = 1