Can the quadratic polynomial x2 + kx + k have equal zeroes for some odd integer k > 1?
Solution A Quadratic Equation will have equal roots if it satisfies the condition given below: b² – 4ac = 0... View Article
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If on division of a non-zero polynomial p (x) by a polynomial g (x), the remainder is zero, what is the relation between the degrees of p (x) and g (x)?
Solution In order to divide p(x) by g(x) We know that, Degree of p(x) > degree of g(x) or Degree... View Article
If on division of a polynomial p (x) by a polynomial g (x), the quotient is zero, what is the relation between the degrees of p (x) and g (x)?
Solution We know that, p(x)= g(x) × q(x)+r(x) According to the given details q(x) =0 When q(x)=0, then r(x) is... View Article
What will the quotient and remainder be on division of ax2 + bx + c by px3 + qx2 + rx + s, p ≠ 0?
Solution Degree of the polynomial px3 + qx2 + rx + s is 3 Degree of the polynomial ax2 + bx + c... View Article
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... 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, ax3 + bx2 + cx + d We know... 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... 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 get to know that... 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, αβ... 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... 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... 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... 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... 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... 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... 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... 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... 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... 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... 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... View Article
