Question

1)х²-3х+2=0 2)-2х²+х+15=03)х²-6х+11=04)9х²+12х+4=05)(х-4)²-4х-11​

Answer 1

Ответ:

1)x1=2

x2=1

2)x1=3

x2=-2,5

3)решений нет

4)x=-2/3

5)x²-12x-5

Answer 2

Ответ:

...........................................

Answer 3

To solve these quadratic equations, we can use the quadratic formula:

For a quadratic equation in the form of ax² + bx + c = 0, the quadratic formula is:

x = (-b ± √(b² - 4ac)) / (2a)

Let's apply this formula to each of the equations you provided:

1. x² - 3x + 2 = 0 a = 1, b = -3, c = 2

x = (-(-3) ± √((-3)² - 4(1)(2))) / (2(1)) x = (3 ± √(9 - 8)) / 2 x = (3 ± √1) / 2

There are two solutions: x1 = (3 + 1) / 2 = 4/2 = 2 x2 = (3 - 1) / 2 = 2/2 = 1

So, the solutions are x1 = 2 and x2 = 1.

2. -2x² + x + 15 = 0 a = -2, b = 1, c = 15

x = (-1 ± √(1² - 4(-2)(15))) / (2(-2)) x = (-1 ± √(1 + 120)) / (-4) x = (-1 ± √121) / (-4)

There are two solutions: x1 = (-1 + 11) / (-4) = 10 / (-4) = -5/2 x2 = (-1 - 11) / (-4) = -12 / (-4) = 3

So, the solutions are x1 = -5/2 and x2 = 3.

3. x² - 6x + 11 = 0 a = 1, b = -6, c = 11

x = (-(-6) ± √((-6)² - 4(1)(11))) / (2(1)) x = (6 ± √(36 - 44)) / 2 x = (6 ± √(-8)) / 2

Since the discriminant (√(-8)) is negative, there are no real solutions to this equation. The solutions are complex:

x1 = (6 + √(-8)) / 2 = (6 + 2i√2) / 2 = 3 + i√2 x2 = (6 - √(-8)) / 2 = (6 - 2i√2) / 2 = 3 - i√2

4. 9x² + 12x + 4 = 0 a = 9, b = 12, c = 4

x = (-12 ± √(12² - 4(9)(4))) / (2(9)) x = (-12 ± √(144 - 144)) / 18 x = (-12 ± √0) / 18

Since the discriminant is zero, there is only one real solution:

x = -12 / 18 = -2/3

5. (x - 4)² - 4x - 11 = 0 This equation can be simplified and solved as follows:

(x - 4)² - 4x - 11 = 0 Expand (x - 4)²: x² - 8x + 16 - 4x - 11 = 0 Combine like terms: x² - 12x + 5 = 0

Now, use the quadratic formula with a = 1, b = -12, and c = 5:

x = (-(-12) ± √((-12)² - 4(1)(5))) / (2(1)) x = (12 ± √(144 - 20)) / 2 x = (12 ± √124) / 2 x = (12 ± 2√31) / 2

Simplify the fraction by dividing both the numerator and denominator by 2:

x = 6 ± √31

So, the solutions are x = 6 + √31 and x = 6 - √31.