1. If one zero of the polynomial ( a^{2} + 9 ) x^{2} + 13x +6a is a reciprocal of the other, find the values of a. Also find the polynomial..

2. Factorise p(x) = x^{3} - 3x^{2} - 9x - 5 .

3. If a and b are the zeroes of the quadratic polynomial f (x) = x^{2} - p(x+1) - c, show that (a+1) (b+1) = 1 - c .

4. The polynomial ax^{3} + bx^{2} + x -6 has (x+2) as a factor and leaves a remainder 4 when divided by (x-2). Find 'a' and 'b' .

5. If the polynomial x^{4} - 6x^{3} + 16x^{2} - 25x +10 is divided by another polynomial x^{2} - 2x + k , the remainder comes out to be x+a . Find k and a .

6. Find the zeroes of the polynomial f(x) = x^{3} - 5x^{2} - 16x + 80 , if its two zeroes are equal in magnitude but opposite in sign.

the given polynomial be

if one zero is the reciprocal of the other.

product of the zeroes = 1.

thus a-3 =0 i.e. a =3

thus the value of a is 3.

2.

at x = -1

therefore by the factor theorem : is a factor of p(x).

now dividing p(x) by (x+1)

thus

due to paucity of time it would not be possible for us to solve all your queries. we are providing solution to two of your queries.

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