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Today's calculation of Integral 120

Source: Hosei University entrance exam/Economics 2006

July 8, 2006
calculusintegrationquadraticsalgebracalculus computations

Problem Statement

Let kk be real constants.How many real roots can the following quadratic equation have? x2=−2x+k+∫01∣t+k∣ dt.x^{2}=-2x+k+\int_{0}^{1}|t+k|\ dt.
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