Amara runs a small corner shop. While checking a delivery record, she finds that an unknown quantity \(x\) of tins satisfies the equation \((x-8)(x+3)=0\), ...
Question 1 Report
Amara runs a small corner shop. While checking a delivery record, she finds that an unknown quantity \(x\) of tins satisfies the equation \((x-8)(x+3)=0\), where \(x\) is the number of tins short of a full crate. She keeps this kind of note every week so that she can order stock more accurately for busy weekends.
- Write down the two solutions of this equation. (2)
Answer Details
An equation already given in factorised form, \((x-8)(x+3) = 0\), is solved directly using the fact that a product is zero only when at least one of its factors is zero.
(a) Setting each bracket to zero in turn: \(x - 8 = 0\) gives \(x = 8\), and \(x + 3 = 0\) gives \(x = -3\). So the two solutions are \(x = 8\) or \(x = -3\). [2 marks]
This "zero product" rule - that \(AB = 0\) means \(A = 0\) or \(B = 0\) - is the reason factorising a quadratic is useful for solving it: once written as a product of two brackets, the equation splits into two much simpler linear equations.
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