Question

6х в квадрате+х-1=0   2х в квадрате-5х+3=0   (10х-4)(3х+2)=0   (3х+1)(6-4х)=0

Answer 1

 

1. 6x^2+x-1=0

Дискриминант: D = b2 - 4a*c = 12- 4*6*-1 = 25
Если D>0 то уравнение имеет 2 вещественных корня: 

x1 = (-b+√D) /2а= (-1+√ 25)/12 =0.4

  x2 = (-b-√D)/2а = (-1-√ 25)/12 =-0.5 

 

2.2 x2 - 5 x + 3 = 0
2 x2 -5 x + 3= 0 
2 x2 -5 x + 3= 0 
Дискриминант: D = b2 - 4a*c = -52- 4*2*3 = 1
Если D>0 то уравнение имеет 2 вещественных корня: 

x1 = (-b+√D)/2а = (5+√ 1)/4 =1.5

  x2 = (-b-√D)/2а = (5-√ 1) /4=1 

Answer 2

Let's solve each equation one by one:

1. 6x^2 + x - 1 = 0 We can use the quadratic formula to solve for x: x = (-b ± sqrt(b^2 - 4ac)) / 2a Plugging in the values of a, b, and c from the given equation: x = (-1 ± sqrt(1^2 - 4(6)(-1))) / 2(6) x = (-1 ± sqrt(25)) / 12 x = (-1 ± 5) / 12 So the solutions are x = -1/2 or x = 1/3.

2. 2x^2 - 5x + 3 = 0 We can factor this quadratic equation: 2x^2 - 5x + 3 = (2x - 3)(x - 1) = 0 So the solutions are x = 3/2 or x = 1.

3. (10x - 4)(3x + 2) = 0 This equation is already factored. To find the solutions, we set each factor equal to zero: 10x - 4 = 0 or 3x + 2 = 0 Solving for x: x = 2/5 or x = -2/3.

4. (3x + 1)(6 - 4x) = 0 Again, this equation is already factored. Setting each factor equal to zero: 3x + 1 = 0 or 6 - 4x = 0 Solving for x: x = -1/3 or x = 3/2.

So the solutions for each equation are:

1. x = -1/2 or x = 1/3
2. x = 3/2 or x = 1
3. x = 2/5 or x = -2/3
4. x = -1/3 or x = 3/2.