Maths Book back answers and solution for Exercise questions - Discuss the maximum possible number of positive and negative roots of the polynomial equation

EXERCISE 3.6

1. Discuss the maximum possible number of positive and negative roots of the polynomial equation 9*x*9 - 4*x*8 + 4*x*7 - 3*x*6 + 2*x*5 + *x*3 + 7*x*2 + 7*x *+ 2 = 0.

2. Discuss the maximum possible number of positive and negative zeros of the polynomials *x*2 - 5*x *+ 6 and *x*2 - 5*x *+16 . Also draw rough sketch of the graphs.

3. Show that the equation *x*9 - 5*x*5 + 4*x*4 + 2*x*2 +1 = 0 has atleast 6 imaginary solutions.

4. Determine the number of positive and negative roots of the equation *x*9 - 5*x*8 -14*x*7 = 0 .

5. Find the exact number of real zeros and imaginary of the polynomial *x*9 + 9*x*7 + 7*x*5 + 5*x*3 + 3*x *.

Answers:

1. It has at most four positive roots and at most two negative roots.

2. It has at most two positive roots and no negative roots.

4. It has one positive real root and one negative real root.

5. no positive real roots and no negative real roots.

Tags : Problem Questions with Answer, Solution , 12th Mathematics : UNIT 3 : Theory of Equations

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12th Mathematics : UNIT 3 : Theory of Equations : Exercise 3.6: Descartes Rule | Problem Questions with Answer, Solution

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