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Systems of Quadratic and Linear Equations, in Depth

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Problems 1

How many choices of real constants a,c,da,c,da,c,d are there such that the polynomial x3+9x2+17x+74x^3 + 9 x^2 + 17 x + 74x3+9x2+17x+74 can be written in the form (x2+ax+1)(x+c)…