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.

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

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Explanation: Extremely detailed and understandable

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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