My first problem in 2016!

Algebra Level 4

Given that \(f(x) =a(x-x_1)(x-x_2)\), \(g(x) =dx+c\), and \(F(x)= f(x)+g(x)\). The graph of \(f(x)\) and \(g(x)\) intersect at \((x_1,0)\). If the graph of \(F(x)\) intersects the x-axis only once, find d.

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