You are GIVEN the "appropriate coefficients" because you are given the equations!
In the first problem you are told that the area of the curved portion of the cone is \(\displaystyle \pi rl\) and that the area of the base is \(\displaystyle \pi r^2\). So the "total area" is \(\displaystyle \pi rl+ \pi r^2= 10\). You are asked to solve the quadratic equation \(\displaystyle \pi r^2+ \pi lr- 10= 0\)= for r. The "appropriate coefficients" are \(\displaystyle a= \pi\), \(\displaystyle b= \pi l\), and c= -10. Since you are not given a specific numerical value for l, your answer will not be a number but a function of l.
In the second problem you are told that \(\displaystyle I= 0.025V+ 0.005V^2\). You are asked to find V when \(\displaystyle I= 0.91\) amperes. So you are asked to solve the equation \(\displaystyle 0.005V^2+ 0.025V= 0.91\). You should not have to be told that that is the same as \(\displaystyle 0.005V^2+ 0.025V- 0.91= 0\) and that the "appropriate coefficients" are a= 0.005, b= 0.025, and c= -0.91.
