Question

In the context of calculus, what values of x are often referred to as "roots of brackets"?

a) x = 0, x = 1, and x = −1
b) x = positive integers
c) x = irrational numbers
d) x = negative integers

Answer 1

Roots of brackets often refer to the solutions of a quadratic equation, which can be any real numbers determined by applying the quadratic formula. In some contexts, only positive real roots have physical significance.

Step-by-step explanation:

The term "roots of brackets" in the context of calculus typically refers to the solutions of a quadratic equation, which are the values of x that make the equation ax² + bx + c = 0 true. The roots can be any real number and are not restricted to positive integers, negative integers, or irrational numbers specifically.

To find the roots of a quadratic equation, we use the quadratic formula, which is x = (-b ± √(b² - 4ac)) / (2a). This formula will yield two solutions, one for each sign of the square root. In certain contexts, like chemistry or physics, where the equation models physical phenomena, only one of the roots might be considered valid based on the context of the problem. Sometimes in equilibrium problems in chemistry, only positive and real roots have significance because they represent physically possible concentrations or measurements.