Polynomials Test

Polynomials

This is Polynomials Test-05 for CBSE class 10 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
If \({x^3} + {x^2} - 2x - 3 = (x - 2)({x^2} + ax + b) + 5\), then
  • A
    a = 4 and b = 5
  • B
    a = – 3 and b = – 4
  • C
    a = 3 and b = 4
    Correct
  • D
    a = 5 and b = 6
2
The real number which should be subtracted from the polynomial \(2{x^3} + 5{x^2} - 14x + 10\) so that the polynomial \(2x - 3\) divides it exactly is
  • A
    6
  • B
    – 7
  • C
    7
    Correct
  • D
    – 6
3
If \(\sqrt 2 \) and \( - \sqrt 2 \) are the zeroes of \(2{x^4} - 3{x^3} - 3{x^2} + 6x - 2\), then the other zeroes are
  • A
    2 and \(\frac{1}{2}\)– 2
  • B
    – 2 and –\(\frac{1}{2}\)
  • C
    2 and \(\frac{1}{2}\)
    Correct
  • D
    \(\frac{1}{2}\) and – \(\frac{1}{2}\)
4
The polynomial to be added to the polynomial \({x^4} + 2{x^3} - 2{x^2} + x - 1\) so that the resulting polynomial is exactly divisible by \({x^2} + 2x - 3\) is
  • A
    x + 2
  • B
    x – 2
    Correct
  • C
    2 – x
  • D
    none of these
5
A polynomial of degree ____ is called a quadratic polynomial.
  • A
    0
  • B
    1
  • C
    2
    Correct
  • D
    3
6
A polynomial of degree ____ is called a cubic polynomial.
  • A
    0
  • B
    1
  • C
    3
    Correct
  • D
    2
7
A polynomial of degree ____ is called a linear polynomial.
  • A
    1
    Correct
  • B
    3
  • C
    2
  • D
    0
8
A polynomial of degree ‘n’ has
  • A
    at most ‘n’ zeroes
    Correct
  • B
    ‘n’ zeroes
  • C
    one zero
  • D
    at least ‘n’ zeroes
9
The degree of a constant polynomial is
  • A
    3
  • B
    2
  • C
    1
  • D
    0
    Correct
10
The largest power of ‘x’ in p(x) is the _________ of the polynomial.
  • A
    solution
  • B
    zero
  • C
    degree
    Correct
  • D
    root
11
Which of the following expressions is not a polynomial?
  • A
    \(5{x^3} - 3{x^2} - \sqrt x + 2\)
    Correct
  • B
    \(5{x^3} - 3{x^2} - x + \sqrt 2 \)
  • C
    \(\sqrt 5 {x^3} - \frac{3}{5}x + \frac{1}{7}\)
  • D
    \(5{x^2} - \frac{2}{3}x + 2\sqrt 5 \)
12
The degree of the polynomial \(5{x^3} - 3{x^2} - x + \sqrt 2 \) is
  • A
    3
    Correct
  • B
    0
  • C
    2
  • D
    1
13
The degree of a biquadratic polynomial is
  • A
    1
  • B
    4
    Correct
  • C
    2
  • D
    3
14
If a polynomial of degree five is divided by a quadratic polynomial, then the degree of the quotient polynomial is
  • A
    0
  • B
    3
    Correct
  • C
    2
  • D
    1
15
If \(a - b\), \(a\) and \(a + b\) are zeroes of the polynomial \({x^3} - 3{x^2} + x + 1\), then the value of \(a + b\) is
  • A
    3
  • B
    \( - 1 + \sqrt 2 \)
  • C
    \(1 \pm \sqrt 2 \)
    Correct
  • D
    \( - 1 - \sqrt 2 \)