Forum

Polynomials

The zeroes of the quadratic polynomial x² + kx + k, k ≠ 0,

(A) cannot both be positive (B) cannot both be negative (C) are always unequal (D) are always equal

Polynomials

The zeroes of the quadratic polynomial x² + 99x + 127 are
(A) both positive (B) both negative
(C) one positive and one negative (D) both equal

Polynomials

If  one  of  the  zeroes  of  the  cubic  polynomial  x³  +  ax²  +  bx  +  c  is  –1,  then  the product of the other two zeroes is

(A) b – a + 1 (B)  b – a – 1 (C)  a – b + 1   (D)  a – b –1

Polynomials

The number of polynomials having zeroes as –2 and 5 is
(A) 1 (B) 2 (C) 3 (D) more than 3

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.