\( 4 \times \) Find the root(s) of the equation \( x^{2}=121 \)

To find the roots of the equation \( x^{2} = 121 \), you simply take the square root of both sides. This results in \( x = \pm \sqrt{121} \). Since the square root of 121 is 11, the solutions are \( x = 11 \) and \( x = -11 \). Thus, the equation has two roots: 11 and -11! Now, let's consider the unique aspect of having two solutions here. In mathematical terms, this is known as the property of quadratic equations, where the graph of the equation typically forms a parabola. Given that the parabola opens upwards (since the coefficient of \( x^2 \) is positive), the two roots represent the points where the parabola intersects the x-axis. Such intersections are fascinating in many real-world applications, like determining the optimal outcomes in economic models or analyzing projectile motion in physics!