Real Numbers

Sample Papers 2013 –BelieveNext.blogspot.com
Sample Papers 2013 –BelieveNext.blogspot.com
1. Find a quadratic polynomial, the sum and product of whose zeroes are 0 and √5 respectively.
2. Find the quadratic polynomial, the sum and product of whose zeroes are 4 and 1, respectively
3. If a and b are the zeros of the quadratic polynomial f(x)= x2-5x+4, find the value of 1/a + 1/b-2a b
4. Find the zeroes of the quadratic polynomial 4√3 x2+ 5 x - 2 √3 and verify the relationship between the zeroes and the coefficients.
5. Find the zeroes of the quadratic polynomial 4u2+ 8u and verify the relationship between the zeroes and the coefficients
6. Find the quadratic polynomial, the sum and product of whose zeroes are √2 and 3 respectively.
7. If a and b are the zeros of the given quadratic polynomial f(x)= 5x2- 7x + 1, find the value 1/a +
1/b
8. Find the zeroes of the polynomial x2– 3 and verify the relationship between the zeroes and the Coefficients
9. Find the remainder when p(x)= x3-6x2+2x-4 when divided by 1 - 2x.
10. Find the remainder when x51+51 is divided by (x+1).
11. Find all the integral zeros of x3-3x2- 2x + 6
12. Obtain all zeros of 3x4+ 6x3- 2x2- 10x - 5, if two of its zeros are √5/√3 and - √5/√3
13. If (x - 2) and [x – ½ ] are the factors of the polynomials qx2+ 5x + r prove that q = r
14. If the zeroes of the polynomial are 3x2− 5x + 2 are a+ b and a- b, find a and b.
15. On dividing 2x2+ 3x + 1 by a polynomial g(x), the quotient and the remainder were 2x-1 and 3 respectively. Find g