Question

Решить уравнение x^2 -2x +5 = 0

Answer 1

D=b^2-4ac=4-20=-16

D<0 следовательно, решений нет

Answer 2

$x {}^{2} - 2x + 5 = 0 \\ d = b { }^{2} - 4ac = \\ = 4 - 4 \times 25 = 4 - 100 = - 96$
корней нет

Answer 3

To solve the quadratic equation $x^2 - 2x + 5 = 0$, we can use the quadratic formula:

The quadratic formula states that for an equation of the form $ax^2 + bx + c = 0$, the solutions for $x$ are given by:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

In this case, $a = 1$, $b = -2$, and $c = 5$. Now, we can plug these values into the quadratic formula:

$x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4 \cdot 1 \cdot 5}}{2 \cdot 1}$

Simplifying further:

$x = \frac{2 \pm \sqrt{4 - 20}}{2}$ $x = \frac{2 \pm \sqrt{-16}}{2}$

Since the term inside the square root ($-16$) is negative, the equation has no real solutions. Instead, it has complex solutions. The square root of a negative number can be represented using the imaginary unit $i$, where $i^2 = -1$.

So, the solutions for $x$ are:

$x = \frac{2 + \sqrt{-16}}{2} = \frac{2 + 4i}{2} = 1 + 2i$

$x = \frac{2 - \sqrt{-16}}{2} = \frac{2 - 4i}{2} = 1 - 2i$

Therefore, the solutions to the equation $x^2 - 2x + 5 = 0$ are $x = 1 + 2i$ and $x = 1 - 2i$.