Write down the Sylvester matrix of the two polynomials [br]f(x)=x[sup]2[/sup]−1,g(x)=x[sup]2[/sup]−4x+3[br]and compute its determinant (you may use [url=https://www.symbolab.com/solver/matrix-determinant-calculator]https://www.symbolab.com/solver/matrix-determinant-calculator Links to an external site.[/url]to save time or check your answer.) What can you conclude about these polynomials based on your computation?[br][br][img]data:image/png;base64,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[/img][br]The determinant of the Sylvester matrix of two polynomials is their resultant, which is zero when the two polynomials have a common root.[br][br]See below for the common root of these two polynomials:[br]