After learning the quadratic formula, many students complain that they were firs

Question

After learning the quadratic formula, many students complain that they were first made to learn how to solve quadratic equations “the hard way” by factoring, taking the square root, and completing the square. Discuss how each of the first two hard ways can actually be easier and more efficient for solving certain types of quadratic equations Discuss the relationship between completing the square and the quadratic formula Explain why it is important to be exposed to the first way before you can fully understand the second way

Explanation / Answer

First way: Factor or square root method

Second way: formula

First way helps visualize the roots easier without even calculating by factoring the constant terms most of the times.

Also it gives an understanding whether the roots are real or complex or imaginary or same etc.

Second way is just formula which confirms the learning from the first method.

e.g. if D = b^2 - 4ac < 0 it means the roots are not real. can be confirmed by both the methods.

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