Final answer:
The quadratic formula is used to solve for the roots of a quadratic equation, ax² + bx + c = 0, when factoring is not possible or too complex. This formula is applied by substituting the coefficients a, b, and c into the formula x = (-b ± √(b² - 4ac)) / (2a). It is a reliable method for finding the solution to any quadratic equation.
Step-by-step explanation:
The quadratic formula is used when solving equations of the form ax² + bx + c = 0, where a, b, and c are coefficients and ‘x’ represents the variable. Mathematical functions of this type are known as second-order polynomials or quadratic functions. To solve such equations, which are called quadratic equations, one would apply the quadratic formula which is x = (-b ± √(b² - 4ac)) / (2a). For example, to solve the equation x² + 1.2 x 10^-2x - 6.0 × 10^-3 = 0, we can use this formula by identifying a, b, and c from the equation and substituting them into the formula to find the value(s) for x.
However, before jumping to the quadratic formula, it is advisable to first check if the equation can be simplified or factored easily. For instance, if the equation can be factored into a product of binomials, this method should be used instead as it's typically simpler and faster. When simplification or factoring isn't possible or is too complex, the quadratic formula is the go-to method to find the roots of the equation.