Chapter 2 – Polynomials

If a polynomial p(y) is divided by y + 2, then which of the following can be the remainder:

If a polynomial p(x) is divided by b – ax; the remainder is the value of p(x) at x =

If the polynomials \(ax^{3} + 4x^{2} + 3x – 4\) and \(x^{3} – 4x + a\), leave the same remainder when divided by (x – 3), then value of a is :

If p(x) = \(2x^{4} – ax^{3} + 4x^{2} + 2x + 1\) is a. multiple of 1 – 2x, then find the value of a :

If -2 is a zero of p(x) = \((ax^{3} + bx^{2} + x – 6)\) and p(x) leaves a remainder 4 when divided by (x – 2), then the values of a and b are (respectively):

If x101 + 1001 is divided by x + 1, then remainder is:

If one zero of a polynomial p(x) = \(ax^{2}\) + bx + c(a ≠ 0) is zero, then, which of the following is correct:

If α, s are the zeroes of \(x^{2}\) – lx + m, then \(\frac{α}{s}\) + \(\frac{s}{α}\)

sum of the squares of the zeroes of the polynomial p(x) = \(x^{2}\) + 7x – k is 25, find k.

If one zero of \(3x^{2} – 8x + 2k + 1\) is seven times the other, find k.

Let, α, s, v be the zeroes of \(x^{3} + 4x^{2} + x- 6\) such that product of two of the zeroes is 6. Find the third zero.

If a, s are the zeroes of \(x^{2} – 8x + λ\), such that α – s = 2, then X =

Find a and b so that the polynomial \(6x^{4} + 8x^{3} – 5x^{2} + ax + b\) is exactly divisible by \(2x^{2} – 5\).

If α, s are the zeroes of p(x) = \(2x^{2} – 5x + 7\), write a polynomial with zeroes 2α+3s and 3α+2s.

If sum of the two zeroes of a cubic polynomial x^{3} – \(ax^{2} + bx – c\), is zero, then which of the following is true:

If a, s are the zeroes of p(x) = \(2x^{2} + 5x + k\) such that, \(α^{2}+ s^{2}+ αs\) = \(\frac{21}{4}\), then k equals,

If α, s are the zeroes of \(x^{2} + px + q\), then a polynomial having zeroes \(\frac{1}{α}\) and \(\frac{1}{s}\) is,

Find the number of zeros in the graph given:

Write the zero of the polynomial p(x), whose graph is given :

If α, s, v are the zeros of the polynomial \(2x^{3} – x^{2} + 3x -1\), find the value of (αsv) + (αs + sv + vα).

If the zeros of the polynomial \(x^{3} – 3x^{2} + x +1\) are p – q,p and p + q. Find the value of q.

A quadratic polynomial has :

If α, s are the roots of cx^{2} – bx + a = 0 (c 0), then α + s is:

If P(x) and D(r) are any two polynomials such that D(x) ≠ 0, there exists unique polynomial Q(x) and R(x) such that, P(x) = D(x). Q(x) + R(x) where :

When we divide \(x^{3}\) + 5x + 7 by \(x^{4} – 7x^{2} – 6\) then quotient and remainder are (respectively):

The value of b, for which \(2x^{3} + 9x^{2} – x – b\) is exactly divisible by 2x + 3 is:

If α and s are two zeros of the polynomial p(x), then which of the following is a factor of p(x):

Find a cubic polynomial with the sum, sum of the product of its zeros taken two at a time and the product of its zeros as -2, +5, -3, respectively.

Write a polynomial with zeros 1, – 1 and 1.