Question

3х в квадрате-3х+4=0

Answer 1

Если дискриминант отрицательный, то из отрицательного числа квадратный корень не извлекается. Это означает, что решений нет.

Answer 2

$3x^{2}-3x+4=0$

$D= b^{2}-4ac= (-3)^{2} -4*3*4=9-48=-39$

Ответ: корней нет.

Answer 3

To solve the quadratic equation $3x^2 - 3x + 4 = 0$, you can use the quadratic formula:

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

In this equation, $a$, $b$, and $c$ are the coefficients of the quadratic equation $ax^2 + bx + c = 0$.

For your equation $3x^2 - 3x + 4 = 0$, you have:

$a = 3, \quad b = -3, \quad c = 4$

Now, plug these values into the quadratic formula:

$x = \frac{-(-3) \pm \sqrt{(-3)^2 - 4(3)(4)}}{2(3)}$

Simplify the expression inside the square root:

$x = \frac{3 \pm \sqrt{9 - 48}}{6}$

Since the expression inside the square root is negative ($9 - 48 = -39$), the solutions will involve imaginary numbers. You can simplify it further using the imaginary unit $i$, where $i^2 = -1$:

$x = \frac{3 \pm \sqrt{39}i}{6}$

So, the solutions for the equation $3x^2 - 3x + 4 = 0$ are:

$x = \frac{3 + \sqrt{39}i}{6} \quad \text{and} \quad x = \frac{3 - \sqrt{39}i}{6}$