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I realize many students have a challenge with presenting the solution of proving question. I am going to illustrate the correct way using the following question.
Show that is always positive for all real values of x.
=> what is always +ve? the values of y not x ( x can be of any values)
=> The graph will not touch x-axis; it is "hanging" above the x-axis
=> No roots, hence discriminant is less than 0
TIPS FOR SHOWING/PROVING QUESTION
- Have an end in your mind. Be clear of the underlying concepts that the question is asking you to prove. Work towards that. For example, in the question, we want to prove that the discriminant is less than 0. <== this is the end.
- Sketch to have a clearer idea.