If a curve is going to be always positive for all real values of x (I am referring to the equation before b2 - 4ac line), then the curve will never hit the x-axis at all, causing no real roots.

Whose solution is this? Some teachers do not accept this method of analysis. Instead, they want the student do completing the square method. Anyway, be careful about use of term. This is an expression. It is not a curve.

In fact, most teachers would advocate the use of discriminant of roots for this question.

Well, he has to probably relate the expression to a curve anyway since not every student understands the deeer implication of “no real roots”

It is good to note that you also agree that "most" teachers" advocate. So the student has to pray hard they are not under the hands of those that do not like using discriminant. Anyway, I won't know too.

it's my teacher's solution, and thank u for the help:)

@Anonymous
Yup, this is a standard solution for the question at the O Levels. You can refer to the other tutor’s posted solution for explanations (since I have no idea how to plot a graph in this chat box).



@Yong Kc
It’s quite tough, actually, to pinpoint a specific idea required for a question. Unfortunately, there is not always a standardised approach in solving questions. Again, you never know if the teacher would accept a student using completing the square.

Some schools require that R-formula, for example, be done from scratch. Some schools require students to do no more than applying formulae. Students who have learnt to avoid writing the extra steps might get a rude shock when realising that the answer key contained the extra steps and so on. On the other hand, students who have learnt to write it out lament at the redundance of the steps in an answer key.

There are many of these instances where there is no clear saying on “who is more correct”.

A student, in my opinion, should not be penalised for getting marked wrong in mathematics just because what they have learnt is logical but the working does not follow the required steps.

In other words, using either approach is logical and should be treated as equally valid.

Agree. This is the minor thing that distinhuish the actual understanding of concept from learn a shortcut method without knowing what is going on. Completing the square is in syllabus. Students suppose to know it is to determine max n min value. So the min value greater than zero.

Both methods are acceptable.

The discriminant method is more commonly seen, by a very large margin.

Ultimately, it is not up to the teachers' preference at O levels, but rather Cambridge Assessment's standards and requirements.