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Concept explainers
Describe the advantages and disadvantages of each method solving quadratic equations.
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Answer to Problem 58HP
The method we will choose according to the
Explanation of Solution
Given:
Describe the advantages and disadvantages of each method solving quadratic equations. Which method do you prefer, and why?
Concept Used:
Factoring:
Factoring is easy if the polynomial is factorable and complicated if it is not factorable. Not all the equations are factorable.
For example
However,
Graphing:
Graphing only gives approximate answers, but it is easy to see the number of solutions. Using square roots is easy when there is no x − term.
For example, for the quadratic You can see the two solutions in the graph. However, it will be difficult to identify the solution x = 8.25780 and 0.24219 in the graph. | Graph of |
Completing square:
Completing square can be used for any quadratic equation and exact solutions can be found, but the leading coefficient has to be 1 and and x2 term must be isolated. It is also easier if the coefficient of the x − term is even; if not, the calculations become harder when dealing with fractions.
For example
Quadratic Formula:
The quadratic Formula will work for any quadratic equation and exact solutions can be found. This method can be time consuming, especially if an equation is easily factored.
For example, use the quadratic Formula to find the solutions of
Thus,
Chapter 9 Solutions
Algebra 1
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