A shopkeeper finds that the number of loaves sold in a day, \(n\), satisfies the equation \(n^2 - 9n = 0\). Solve the equation to find the two possible valu...
Question 1 Report
A shopkeeper finds that the number of loaves sold in a day, \(n\), satisfies the equation \(n^2 - 9n = 0\).
- Solve the equation to find the two possible values of \(n\). (1)
- Explain which value of \(n\) fits the context, and write down this value. (1)
Answer Details
This question factorises a quadratic with no constant term and then interprets which root makes sense for a real quantity.
Taking out the common factor \(n\):
\[n(n-9) = 0\]so \(n = 0\) or \(n = 9\) [1 mark].
A day with \(0\) loaves sold would not be a meaningful day of trading in this context, so \(n=0\) does not fit; the value that fits is \(n = 9\) [1 mark].
Whenever a quadratic has no constant term, factorising out the common factor \(n\) is quicker than using the quadratic formula, and always gives \(n=0\) as one of the two roots.
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