Problem 1 :
Discuss the maximum possible number of positive and negative roots of the polynomial equation
9x^{9} - 4x^{8} + 4x^{7} - 3x^{6} + 2x^{5} + x^{3} + 7x^{2} + 7x + 2 = 0
Problem 2 :
Discuss the maximum possible number of positive and negative zeros of the polynomials
x^{2} - 5x + 6 and x^{2} - 5x + 16.
Also draw rough sketch of the graphs.
Problem 3 :
Show that the equation
x^{9} - 5x^{5} + 4x^{4} + 2x^{2} + 1 = 0
has atleast 6 imaginary solutions.
Problem 4 :
Determine the number of positive and negative roots of the equation
x^{9} - 5x^{8} - 14x^{7} = 0
Problem 5 :
Find the exact number of real zeros and imaginary of the polynomial
x^{9} + 9x^{7}+ 7x^{5} + 5x^{3} + 3x
1) So, at least 4 positive real roots, at least 3 negative real roots and 2 imaginary roots will be there.
2) Therefore it has atleast 2 positive roots and no negative roots.
3) it has atleast 6 imaginary roots.
4) the given polynomial will have atleast 1 positive root, 1 negative root and 7 imaginary roots.
5) the given polynomial will have no positive, no negative and 9 imaginary roots.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM