Show that x19 + x8 + 1 has multiple zeros in some extension of Z3.

Q: Show that the square of any integer is of the form 3m or 3m+1 but not of form 3m+2.

A: Proof :-

Q: According to Descartes' Rule of Signs, how many negative zeroS could the polynomial æ4 – 3x³ – 2x² +…

A: According to Descartes's rule of signs, maximum number of positive real root of a polynomial…

Q: Determine an integer to replace the blank in the polynomial 49x? - 84xy + so that the trinomial is a…

A: Since (a-b)2=a2-2ab+b2

Q: Show that the polynomial x5 - 6x + 3 over Q is not solvable byradicals.

A:

Q: label the  polynominals of X2 - 18x + 32 =0

A:

Q: According to the Factor Theorem, which are zeros of f(x)=2x^3−22x^2+72x−72 given that (x−6) is a…

A: Given problem:- According to the Factor Theorem, which are zeros of f(x)=2x3 −22x2 +72x−72 given…

Q: what could be a polynomial with a degree of 5 if its zeros are -2,1, and 4?

A: The given zeros are, –2, 1 and 4.

Q: Write the quadratic Q = x1x2 + 4x1x3 – 12x2x3 + 9x2x4 + 5x – 18x3X4 + x? in quadratic form x² A x ,…

A: Given:  Q=x1x2+4x1x3-12x2x3+9x2x4+5x32-18x3x4+x42 Let x=x1x2x3x4 As there are 4 variables, so take A…

Q: Select the polynomial that has exactly three zeros O - 111 O 4x + 11x O 22 - 3x? + 2x2 2 x² 2x 8 -…

A: we know that if polynomial has n degree then there are at most solutions. here in option A…

Q: why do I multiply m with(x2-x1)?

A: see  below the explanation and answer

Q: Show that a cubic polynomial x3 + Ax2 + Bx + C has one real zero and two pure imaginary zeros only…

A:

Q: State the discriminant of 6x2-2x+K

A: Quadratic equaton is  6x2-2x+K=0