Archives

Can x² – 1 be the quotient on division of x⁶ + 2x³ + x – 1 by a polynomial in x of degree 5?

Solution No, x2 – 1 cannot be the quotient on division of x6 + 2x3 + x – 1 by a polynomial in x of degree 5.... View Article

Given that one of the zeroes of the cubic polynomial ax³ + bx² + cx + d is zero, the product of the other two zeroes is (A) (-c/a) (B) c/a (C) 0 (D) (-b/a)

Solution (B) (c/a) Option (B) is the correct answer Explanation: According to the given details We have the polynomial,... View Article

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

Answer: (D) more than 3 Polynomial is made up of two terms, namely Poly and Nominal. A polynomial is defined as an expression that is composed... View Article

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

Solution (D)a = 2, b = – 6 option (D) is the correct answer. Explanation: According to the given details we... View Article

A quadratic polynomial, whose zeroes are -3 and 4, is (A) x² – x + 12 (B) x² + x + 12 (C) (x²/2)-(x/2)-6 (D) 2x² + 2x -24

Solution (C) (x2/2)-(x/2)-6 option (C) is the correct answer. Explanation: Sum of zeroes, α+ β= -3+4 =1 Product of Zeroes,... View Article

If one of the zeroes of the quadratic polynomial (k-1) x² + k x + 1 is -3, then the value of k is (A) 4/3 (B) -4/3 (C) 2/3 (D) -2/3

Solution (A) 4/3 option (A) is the correct answer. Explanation: According to thegiven details -3 is one of the zeros of quadratic... View Article

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

Given that n, n + 2 and n + 4 three integer where n is any positive integer To Prove One and only one out of n, n + 2 and n + 4 is... View Article

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.

Given that Positive integer of the form 6q + r, q is an integer To Prove The cube of a positive integer of the form 6q + r, q is an... View Article

Prove that if x and y are both odd positive integers, then x² + y² is even but not divisible by 4.

Given that x and y are both odd positive integers To Prove x2 + y2 is even but not divisible by 4 Proof Let the two odd positive... View Article

Show that the square of any odd integer is of the form 4q + 1, for some integer q.

Given that Any integer m To Prove We need to prove that the square of any odd integer is of the form 4q + 1, Proof Let a be any odd integer... View Article

Show that the square of any positive integer cannot be of the form 6m + 2 or 6m + 5 for any integer m.

Given that Any integer m To Prove We need to prove that the square of any positive integer cannot be of the form 6m + 2 or 6m + 5 for any... View Article

Show that the square of any positive integer cannot be of the form 5q + 2 or 5q + 3 for any integer q.

Given that Some integer q To Prove We need to prove that the square of any positive integer cannot be of the form 5q + 2 or 5q... View Article

Show that cube of any positive integer is of the form 4m, 4m + 1 or 4m + 3, for some integer m.

Given that Some integer m To Prove We need to prove that the cube of any positive integer is of the form 4m, 4m + 1 or 4m + 3, for some... View Article

Show that the square of any positive integer is either of the form 4q or 4q + 1 for some integer q.

Given that Some integer q To Prove We need to prove that he square of any positive integer is either of the form 4q or 4q + 1 for some... View Article

A positive integer is of the form 3q + 1, q being a natural number. Can you write its square in any form other than 3m + 1, i.e., 3m or 3m + 2 for some integer m? Justify your answer.

Solution: No, its square in any form other than 3m + 1, i.e., 3m or 3m + 2 for some integer m. Justification Consider the positive... View Article

Write whether the square of any positive integer can be of the form 3m + 2, where m is a natural number. Justify your answer.

Solution: No, the square of any positive integer cannot be written in the form 3m + 2 where m is a natural number Justification: According to... View Article

M	T	W	T	F	S	S
						1
2	3	4	5	6	7	8
9	10	11	12	13	14	15
16	17	18	19	20	21	22
23	24	25	26	27	28	29
30	31