Question 863165
Too many questions in one posting, but there is a lesson  which will help with the mixture problem, and I give here most of the solution for your quadratic equation problem.


See this for the mixture problem:  <a href="http://www.algebra.com/tutors/Two-Part-Mixture-with-one-material-quantity-unknown.lesson?content_action=show_dev">Mixture percents: One part known, other part unknown</a>



The quadratic, k value question:
{{{kx^2 + 26x + k = 0}}}
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The discriminant must be 0, if the equation has exactly 1 solution.
Given {{{ax^2+bx+c}}}, the discriminant is {{{b^2-4ac}}}.
{{{26^2-4*k*k=0}}}
{{{4k^2=26^2}}}
{{{k^2=26^2/4}}}
{{{k^2=(26/2)^2}}}
{{{k^2=13^2}}}
{{{highlight(k=-13)}}} or {{{highlight(k=13)}}}



Number 4 Question:
How many pounds bought, if no scale error?  2 pounds.
If the scale undershoots, then reading was 2-0.09 pounds, 1.91 pounds.
If scale overshoots, then reading was 2.09 pounds.
The expectation is $11.00 dollars for 2 pounds of coffee.
The undershot at 1.91 pounds SHOULD cost {{{1.91*5.50=10.51}}} dollars.  Payment is 45 cents too much.
The overshot at 2.09 pounds SHOULD cost {{{2.09*5.50=11.50}}} dollars.  Payment is 50 cents too little.