The roots of the quadratic equation $$6x^2$$​ - x - 2 = 0 are

Correct option is C

Given:

The quadratic equation is:

$$6x^2 - x - 2 = 0$$​

Formula Used:

To find the roots of a quadratic equation a$$x^2$$​ + bx + c = 0, we use the quadratic formula:

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

Where:

- a is the coefficient of $$x^2$$​,

- b is the coefficient of x,

- c is the constant term.

Solution:

1. Identify the coefficients:

From the given equation 6$$x^2$$​ - x - 2 = 0:

a = 6, b = -1, c = -2

2. Substitute into the quadratic formula:

$$x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4(6)(-2)}}{2(6)}$$​

Simplify step-by-step:

$$x = \frac{1 \pm \sqrt{1 - 4(6)(-2)}}{12}$$​

$$x = \frac{1 \pm \sqrt{1 + 48}}{12}$$​

$$x = \frac{1 \pm \sqrt{49}}{12}$$​

3. Simplify the square root:

$$x = \frac{1 \pm 7}{12}$$​

4. Find the two roots:

For x = $$\frac{1 + 7}{12}$$​

x = $$\frac{8}{12} = \frac{2}{3}$$​

For x = $$\frac{1 - 7}{12}$$​:

x = $$\frac{-6}{12} = \frac{-1}{2}$$​

Final Answer:

The roots of the quadratic equation are:

$$x = \frac{2}{3}$$, $$x = \frac{-1}{2}$$​