Question

A) x2 - 8x - 33 = 0;6) 16x2 - 24x + 9 = 0;B) x2 + 4x + 5 =0 ;r) -6x2 + 5x - 1 -0.​

Answer 1

Ответ:

а)

11

х = - —

2

б)

9

х = - —

8

в)

5

х = - —

6

г)

х = - 7х - 1

Answer 2

It seems like you've provided two sets of quadratic equations, and you'd like to find the solutions for each set. Let's solve them one by one:

A) x^2 - 8x - 33 = 0

To solve this quadratic equation, you can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this equation, a = 1, b = -8, and c = -33. Plugging these values into the formula:

x = (-(-8) ± √((-8)² - 4(1)(-33))) / (2(1)) x = (8 ± √(64 + 132)) / 2 x = (8 ± √196) / 2 x = (8 ± 14) / 2

Now, you have two possible solutions:

1. x = (8 + 14) / 2 = 22 / 2 = 11
2. x = (8 - 14) / 2 = -6 / 2 = -3

So, the solutions to the equation x^2 - 8x - 33 = 0 are x = 11 and x = -3.

6) 16x^2 - 24x + 9 = 0

This quadratic equation appears to be a perfect square trinomial. It factors as follows:

(4x - 3)(4x - 3) = 0

Now, set each factor equal to zero:

4x - 3 = 0 4x - 3 = 0

Solve for x in each equation:

1. 4x - 3 = 0 4x = 3 x = 3/4

So, the solution to the equation 16x^2 - 24x + 9 = 0 is x = 3/4.

B) x^2 + 4x + 5 = 0

To solve this quadratic equation, you can again use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this equation, a = 1, b = 4, and c = 5. Plugging these values into the formula:

x = (-4 ± √(4² - 4(1)(5))) / (2(1)) x = (-4 ± √(16 - 20)) / 2 x = (-4 ± √(-4)) / 2

Since the discriminant (the value inside the square root) is negative, there are no real solutions to this equation. The solutions will be complex numbers:

x = (-4 ± 2i) / 2

Now, simplify:

1. x = (-4 + 2i) / 2 = -2 + i
2. x = (-4 - 2i) / 2 = -2 - i

So, the solutions to the equation x^2 + 4x + 5 = 0 are x = -2 + i and x = -2 - i.

r) -6x^2 + 5x - 1 = 0

To solve this quadratic equation, you can again use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this equation, a = -6, b = 5, and c = -1. Plugging these values into the formula:

x = (-5 ± √(5² - 4(-6)(-1))) / (2(-6)) x = (-5 ± √(25 - 24)) / (-12) x = (-5 ± √1) / (-12)

Now, simplify:

1. x = (-5 + 1) / (-12) = -4 / (-12) = 1/3
2. x = (-5 - 1) / (-12) = -6 / (-12) = 1/2

So, the solutions to the equation -6x^2 + 5x - 1 = 0 are x = 1/3 and x = 1/2.