Monday, 11 March 2013

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 imaginary

Substituting 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.

1. - Explanation shows complete and clear understanding of the concept.
- Very clear and detailed explanation
- Work is presented neatly.
Well done^_^

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

Explanation - 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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4. Understood the question , able to state the explanation of the steps . Understood that D≥0 and has successfully proven it with perfect square

Could 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)

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

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

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

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

-Working is neat and comprehensible, shows substitution.

-Organisation is very eminent. Easy to read and understand

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

10. Clear and easy to understand presentation
Wrote down the coefficients which are good
Concepts are clear and very straightforward

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

12. Concept: Is clear and presented
Working/Explanation: Clearly presented and not difficult to understand
Organization: Systematic and easy to understand

13. 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. :)