Find the root of the equation 2x\(^2\) - 3x - 2 = 0
Answer Details
To find the root(s) of the quadratic equation 2x\(^2\) - 3x - 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 this case, a = 2, b = -3, and c = -2. Substituting these values into the formula, we get:
$$x = \frac{-(-3) \pm \sqrt{(-3)^2-4(2)(-2)}}{2(2)}$$
Simplifying:
$$x = \frac{3 \pm \sqrt{9+16}}{4}$$
$$x = \frac{3 \pm \sqrt{25}}{4}$$
We can simplify the square root to get:
$$x = \frac{3 \pm 5}{4}$$
So the roots are:
$$x = \frac{3 + 5}{4} = 2$$
$$x = \frac{3 - 5}{4} = -\frac{1}{2}$$
Therefore, the answer is x = -1/2 or 2.