1.Check whether 6n can end with the digit 0 for any natural number n.
2. Prove that √2 is irrational.
3.Show that any positive odd integer is of the form 6q+1 or 6q+3 or 6q+5 where ’q’ is some integer.
4. A quadratic polynomial where roots are -3 and 4 is______________.
5. If the zeroes of the quadratic polynomial x2+ (a+1)x+ b are 2 and -3, then
(a) a=-7 , b=-1
(b)a=5 , b=-1
(c)a=2 , b=-6
(d)a=0 , b=-6
6.What must be added to p(x)=4x2 + 2x3 -2x2+x -1 so that the resulting polynomial is divisible by g(x)= x2 +2x-3?
7.The zeroes of √3x2+10x+7√3 are
(d) none of these
8. Find the zeroes of the polynomial 2x2-9 and verify the relationship between its zeroes and the coefficient of the polynomial.
9. Find all the zeroes of the polynomial x3-6x2+11x-6, if two of its zeroes are 1 and 2.
10. Find the other zeroes of the polynomial x4-5x3+2x2+10x -8 if it is given that two of its zeroes are -√2 and √2.