WAEC - Further Mathematics (2007 - No. 23)
Find the value of p for which \(x^{2} - x + p\) becomes a perfect square.
\(-\frac{1}{2}\)
\(\frac{1}{4}\)
\(\frac{1}{2}\)
\(1\)
Vysvětlení
The equation \(ax^{2} + bx + c\) is a perfect square if \(b^{2} = 4ac\).
\(x^{2} - x + p\)
\((-1)^{2} = 4(1)(p)\)
\(1 = 4p \implies p = \frac{1}{4}\)