Question 2
Write down the Sylvester matrix of the two polynomials
f(x)=x2−1,g(x)=x2−4x+3
and compute its determinant (you may use https://www.symbolab.com/solver/matrix-determinant-calculator Links to an external site.to save time or check your answer.) What can you conclude about these polynomials based on your computation?
The determinant of the Sylvester matrix of two polynomials is their resultant, which is zero when the two polynomials have a common root.
See below for the common root of these two polynomials:
The determinant of the Sylvester matrix of two polynomials is their resultant, which is zero when the two polynomials have a common root.
See below for the common root of these two polynomials: