<p>A curve \(C\) has equation \(\mathrm{f}(x) = \frac{a}{x^2} + bx + c\), where&nbsp;\(a\), \(b\) and \(c\) are constants. It is given that&nbsp;\(C\) passes through the points \((-1, 4)\) and \((2, -11)\) and the curve of \(y = \frac{1}{\mathrm{f}(x)}\) has a vertical asymptote with equation \(x = 1\). Find the equation of \(C\).<span class="inline-marks">[4]</span></p>

A curve \(C\) has equation \(\mathrm{f}(x) = \frac{a}{x^2} + bx + c\), where \(a\), \(b\) and \(c\) are constants. It is given that \(C\) passes through the points \((-1, 4)\) and \((2, -11)\) and the curve of \(y = \frac{1}{\mathrm{f}(x)}\) has a vertical asymptote with equation \(x = 1\). Find the equation of \(C\).

Simultaneous Equations (3 Variables)

International Baccalaureate Higher Level Mathematics

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