Monday, 11 March 2013

Quadratic - Practice 14 (Justin)

Determine the range of values of k for which the function x^2 + 6x + k, is positive for all values of x. 

Keywords:  all values of x.
This tells us that the possible roots of the equation are: Real and different, or Real and equal. 
This is because there needs to be a value for 'x', which means we cannot have the value 'imaginary' as an answer.

Keywords: range ... is Positive
This tells us that k cannot be < 0. the range of k needs to be positive. 

Discriminant D: 
As we have learnt before, 
when roots are real and different... D > 0
when roots are real and equal... D = 0 
when roots are imaginary... D < 0

Thus as our roots are Real, we would use D ≥ 0. 

From the equation: 
a = 1, b = 6, c = k.
When D = b^2 - 4ac

Therefore D = 36 - 4k. 

D ≥ 0
36 - 4k ≥ 0
36 ≥ 4k
k ≤ 9 

However as k > 0, the range is limited to 0 < k ≤ 9.


  1. Explanation is very clear and concise. Understanding is clearly shown. Steps are clear.

  2. The explanation is clear which also explains the question keywords very well. Overall it is easy to understand the answer although it is quite lengthy.

  3. Good explanation, with a look into the concepts of the topic. Steps are clear.

  4. Neatness and Organization: Extremely organized and analyzed question well.
    Mathematical concepts: Very strong, no error.
    Explanation: Extremely detailed and understandable

  5. Explanation is detailed and clear. It shows complete understanding of the concept used to solve the problems. The work is neat, clear, organized fashion that is easy to read.