**Mrs. V.P.Suseela, TGT(Maths)**

**Date of submission: 27 June 2011**

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__REAL NUMBERS__

1.Use euclid’s division algorithm to find the HCF of :

a) 6265 and 76254 b) 3854 and 48250

2. Find HCF and LCM of following using fundamental theorem of arithmetic method :

a) 1376 AND 15428 b) 448,1008 and 168

3) Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or non terminating repeating decimal expansion :

a) 7/9 b) 35/51 c) 63/90

4) Show that for all positive integer to be a perfect square, it should be of the form 8k + 1.

5) Prove that 35 is irrational.

6) Prove that 1**/**3 is irrational.

7) Can we have any n N, where 7^{n} ends with digit zero.

__POLYNOMIALS__

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1) Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and thie coefficient :

a) P(x) = 4x^{2} + 24x + 36

b) P(x) = 25x^{2} + 5x

2) Find a quadratic polynomial whose zeroes are -9 and -1/9.

3) Sum and product of zeroes of quadratic polynomial are 2 and 5 respectively.Find the quadratic polynomial.

4) Find a quadratic polynomial whose one zero is -8 and sum of zeroes is 0.

5)verify that -5,1/2,3/4 are zeroes of cubic polynomial 4x^{3} + 20x +2x -3 also verify the relationship between the zeroes and the coefficient.

6) Divide 24x^{3} + 20x^{2}y^{2} – 4xy by 2xy.

7)Divide ax^{2} + (b+ac) x + bc by x+c.

8) Use division state whether 2y-5 is a factor of 4y^{4} – 10y^{3}– 10y^{2} + 30y – 15.

9)m, n are zeroes of ax^{2} – 5x + a. Find the value of a and c ,if m+n = m.n = 10.