Show that the equation a^2x^2 + 3ax + 2 = 0 always has real roots.

From the equation we know the values of a, b, c.

The discriminant (D) determines the roots of an equation.

if D > 0, the roots are real and distinct

if D = 0, the roots are real and equal

if D < 0, the roots are imaginarySubstituting the values of a,b,c into b^2 - 4ac, we are able to find the value of the discriminant.

a^2 is always more than 0.

Since the value of the discriminant for a^2x^2 + 3ax + 2 is more than 0, we know that its roots are real.

- Explanation shows complete and clear understanding of the concept.

ReplyDelete- Very clear and detailed explanation

- Work is presented neatly.

Well done^_^

Mathematical Concepts - Everything is there except for the explanation why a^2 is always >0 . Maybe show some examples of a (positive, negative , 0 )

ReplyDeleteExplanation - Able to understand the working and all that :D

Presentation - Explained why it always have real roots (D > 0) . Steps all shown clearly .

- Owen

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ReplyDeleteUnderstood the question , able to state the explanation of the steps . Understood that D≥0 and has successfully proven it with perfect square

ReplyDeleteCould have included the perfect squares are always bigger than zero in the working instead of the side note.

Clear organisation , steps are easy to follow and smooth . (Not much skipping between steps)

The mathematical concept is very clear. Steps are in a systematic order and clearly shown. It is very easy for the reader to understand :)

ReplyDeleteThe mathematical concept is clear she explained what the discriminant determines and shows how she arrived at the value of the discriminant.

ReplyDeleteThe explanation could be improved and she could say how a^2>0 by stating that anything squared will be a positive value.

The organisation is good and she clearly stated all the steps she used to get the answer.

Mathematical concepts are clear and workings are organise in a systematic and concise manner,workings is neat and easy to read

ReplyDelete-Presentation is clear and thorough. Just clear mention of how the discriminant affects the nature of the roots

ReplyDelete-Working is neat and comprehensible, shows substitution.

-Organisation is very eminent. Easy to read and understand

The explanations for the mathematical concepts behind each step is clear and the work is neat and orderly.

ReplyDeleteClear and easy to understand presentation

ReplyDeleteWrote down the coefficients which are good

Concepts are clear and very straightforward

Good understanding of math concepts, written down clearly why equation has real roots by showing that D>0, by showing a^2 >0.

ReplyDeleteConcept: Is clear and presented

ReplyDeleteWorking/Explanation: Clearly presented and not difficult to understand

Organization: Systematic and easy to understand

Your explanation is very detailed and comprehendible, and shows that you understand all the topics used to answer. Also, your working is very neat and legible. :)

ReplyDelete