# DESCARTES RULES OF SIGNS PRACTICE WORKSHEET

Problem 1 :

Discuss the maximum possible number of positive and negative roots of the polynomial equation

9x9 - 4x8 + 4x7 - 3x6 + 2x5 + x3 + 7x2 + 7x + 2 = 0

Problem 2 :

Discuss the maximum possible number of positive and negative zeros of the polynomials

x2 - 5x + 6 and x2 - 5x + 16.

Also draw rough sketch of the graphs.

Solution

Problem 3 :

Show that the equation

x9 - 5x5 + 4x4 + 2x2 + 1 = 0

has atleast 6 imaginary solutions.

Solution

Problem 4 :

Determine the number of positive and negative roots of the equation

x9 - 5x8 - 14x7 = 0

Solution

Problem 5 :

Find the exact number of real zeros and imaginary of the polynomial

x9 + 9x7+ 7x5 + 5x3 + 3x

Solution

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.

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