Given that x=1.5 is the only solution to the equation 4x^2 - ax + b = 0, find the values of a and b. Show all workings.
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Answer:
Step-by-step explanation:
The first thing we need to do is to identify the characteristics of this problem. As you can see, this situation has restriction, limitations on how much money and time they can spend.
In mathematics, restrictions are expressed with inequalities, because it gives us the power to express in terms of more or less than something. When we have this inequality-restrictions problems, it's very helpful to organise all info, so according to the problem, we have:
$ hr
Candidates (x) 400 20
Employees (y) 3600 120
Max. 95000 470
We this organisation, we can easily find expressions, the important thing here is to put together similar variables, money with money and time with time.
So, you can see that, the maximum money they can spend is 95000, and the maximum time is 470 hours, which give us:
As you can see, for money inequality, we used < (less than), and for hours we used ''less or equal than''. This difference is because in the text it says that they has less than 95000 (not equal than 95000), and for hours they have at most 470 (meaning that this is a maximum, 470 and below that number).
Therefore, those two inequality express the restriction about money and time limitations for candidates and employees.