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Express $\frac{24}{18-x} - \frac{24}{18+x} = 1$ as a quadratic equation in standard form and find the discriminant of the quadratic equation, so obtained. Also, find the roots of the equation.
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Given equation can be written as
$24(18 + x) - 24(18 - x) = 324 - x^2$ (1 Mark)
i.e., $x^2 + 48x - 324 = 0$ (1 Mark)
$D = 48^2 - 4(-324) = 3600$ (1 Mark)
Roots are $\frac{-48 \pm 60}{2}$ (1 Mark)
i.e., 6, -54 (1/2 Mark)
$24(18 + x) - 24(18 - x) = 324 - x^2$ (1 Mark)
i.e., $x^2 + 48x - 324 = 0$ (1 Mark)
$D = 48^2 - 4(-324) = 3600$ (1 Mark)
Roots are $\frac{-48 \pm 60}{2}$ (1 Mark)
i.e., 6, -54 (1/2 Mark)