Science:Math Exam Resources/Courses/MATH100/December 2015/Question 12 (c)
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Question 12 (c) 

Show that the same equation cannot have more than two solutions. Part (a) will help you here. 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Assume we have more than two solutions and reach to a contradiction by using part (a). 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Assume that the equation in (b) has more than two solutions. In other words, has at least three zeros. Then, by Part (a), must have at least one zero.
cannot have a zero. Therefore, this makes a contradiction, which proves the statement. 