Question

Оба корня уравнения 6х^2-х-2=0

Answer 1

$6 {x}^{2} - x - 2 = 0$
Дискриминант = 1 - 4 *6 *(-2) = 49
$x1 = \frac{1 - \sqrt{49} }{12} = \frac{ - 6}{12} = - 0.5$
$x2 = \frac{ 1 + \sqrt{49} }{12 } = \frac{8}{12} = \frac{2}{3}$
Ответ: -0.5;
$\frac{2}{3}$

Answer 2

6х²-х-2=0

(2х+1)(3х-2) = 0

х₁ = -0,5

х₂ = 2/3

Answer 3

To find the roots of the quadratic equation $6x^2 - x - 2 = 0$, we can use the quadratic formula:

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

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

In our equation, $a = 6$, $b = -1$, and $c = -2$.

Now, plug these values into the quadratic formula:

$x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4 \cdot 6 \cdot (-2)}}{2 \cdot 6}$ $x = \frac{1 \pm \sqrt{1 + 48}}{12}$ $x = \frac{1 \pm \sqrt{49}}{12}$ $x = \frac{1 \pm 7}{12}$

Now, calculate both possible roots:

1. For the positive square root: $x = \frac{1 + 7}{12} = \frac{8}{12} = \frac{2}{3}$

2. For the negative square root: $x = \frac{1 - 7}{12} = \frac{-6}{12} = -\frac{1}{2}$

So, the two roots of the equation $6x^2 - x - 2 = 0$ are $x = \frac{2}{3}$ and $x = -\frac{1}{2}$.