Final answer:
The 'Inhour equation' mentioned does not exist; however, an example of a polynomial with seven roots can be given as a seventh-degree polynomial. Selecting arbitrary roots 1 through 7, an example equation is provided and the importance of checking the reasonableness of the answer is noted.
Step-by-step explanation:
The question appears to contain a typo or a misunderstanding, as there is no widely recognized 'Inhour equation' in mathematics that would provide an equation with seven roots. However, it is possible to create a polynomial equation with seven roots by considering the nature of polynomial functions. For instance, a seventh-degree polynomial would have seven roots (some of which may be complex or repeated). A simple example of a seventh-degree polynomial equation is:
f(x) = (x - r1)(x - r2)...(x - r7)
Where r1, r2, ..., r7 are the seven roots of the polynomial. If we choose arbitrary roots, for example, 1, 2, 3, 4, 5, 6, and 7, our equation would be:
f(x) = (x - 1)(x - 2)(x - 3)(x - 4)(x - 5)(x - 6)(x - 7)
To check if the answer is reasonable, you would substitute the roots back into the polynomial to ensure that it equals zero. Also, remember to eliminate terms wherever possible to simplify the algebra during your calculations.