Forum

Polynomials

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

Polynomials

If one zero of the quadratic polynomial x² + 3x + k is 2, then the value of k is

(A) 10 (B) –10 (C) 5            (D)    –5

Real Numbers

Show that one and only one out of n, n + 4, n + 8, n + 12 and n + 16 is divisible by 5, where n is any positive integer.

Real Numbers

For any positive integer n, prove that n³ – n is divisible by 6.

Real Numbers

Prove that one of any three consecutive positive integers must be divisible by 3.

Real Numbers

Prove that one and only one out of n, n + 2 and  n + 4 is divisible by 3, where n is any positive integer.

Real Numbers

Show that the cube of a positive integer of the form 6q + r, q is an integer and r = 0, 1, 2, 3, 4, 5 is also of the form 6m + r.

Real Numbers

Show that the square of an odd positive integer can be of the form 6q + 1 or 6q + 3 for some integer q.

Real Numbers

Write the denominator of the rational number  257/ 5000 in the form 2m × 5n, where  m, n are non-negative integers. Hence, write its decimal expansion, without actual division.

Real Numbers

On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm  and 45 cm, respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps?