What are the roots of the equation? Answer \( 2 x^{2}-3 x-2=0 \) \( \frac{-3 \pm \sqrt{7}}{4} \) \( \frac{3 \pm \sqrt{7}}{4} \) and \( \frac{1}{2} \) and -2

To find the roots of the equation \( 2 x^{2}-3 x-2=0 \), you can utilize the quadratic formula: \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). For this equation, \( a = 2 \), \( b = -3 \), and \( c = -2 \). Plugging these values in, you’ll calculate the discriminant (the part under the square root), which assists in determining the roots. Once you simplify using the quadratic formula, you'll see that the roots can be expressed as \( \frac{3 \pm \sqrt{25}}{4} \), clearly leading you to \( x = 2 \) or \( x = -\frac{1}{2} \) as the correct roots. Keep an eye out for signs and arithmetic mistakes, as these can lead to confusion in your final answer!