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.



5 comments:

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

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

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  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.

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