Solve : (x - 5) (x - 7) (x + 6) (x + 4) = 504

Find all zeros of the polynomial x⁶- 3x⁵- 5x⁴ + 22x³- 39x²- 39x + 135, if it is known that 1+2i and \(\sqrt{3}\) are two of its zeros.

Solve the following equation: x⁴-10x³+ 26x²-10x + 1 = 0

Solve the equation 6x⁴- 5x³- 38x²- 5x + 6 = 0 if it is known that \(\frac{1}{3}\) is a solution.

Discuss the maximum possible number of positive and negative roots of the polynomial equations x²−5x+6 and x²−5x+16 . Also draw rough sketch of the graphs