Final answer:
To solve a word problem involving a quadratic equation with irrational roots, one uses the quadratic formula. If simplification is possible beforehand, it can make the process easier. Understanding how to perform complex operations like taking roots can be vital, especially in equilibrium problems.
Step-by-step explanation:
When solving a word problem using a quadratic equation, you often end up with an equation in the form ax²+bx+c = 0. To find the irrational roots or solutions, you can use the quadratic formula, which is given by
x = √[-b ± √(b²-4ac)]/(2a)
If the discriminant, b²-4ac, is positive but not a perfect square, the roots will be irrational. In some cases, it's possible to simplify the equation before applying the quadratic formula, for example by factoring if the left side is a perfect square, which can make the process more expedient. However, for more complex equations or those related to equilibrium problems, which may involve square roots or higher roots, it's essential to know how to perform these operations, potentially with a calculator's assistance.