Polynomials Test

Polynomials

This is Polynomials Test-01 for CBSE class 10 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
If the graph of a polynomial intersects the x – axis at three points, then the number of zeroes =
  • A
    at most three
  • B
    at least three
  • C
    3
    Correct
  • D
    0
2
The graph of the polynomial f(x) = 2x – 5 intersects the x – axis at
  • A
    \(\left( {\frac{5}{2}{\text{ }},{\text{ }}\frac{5}{2}} \right)\)
  • B
    \(\left( {\frac{5}{2}{\text{ }},{\text{ }}0} \right)\)
    Correct
  • C
    \(\left( {\frac{5}{2}{\text{ }},{\text{ }} - \frac{5}{2}} \right)\)
  • D
    \(\left( { - \frac{5}{2}{\text{ }},{\text{ }}0} \right)\)
3
The graph of a cubic polynomial x3 – 4x meets the x – axis at ( – 2, 0), (0, 0) and (2, 0), then the zeroes of the polynomial are
  • A
    – 2, 0 and 0
  • B
    0, 0 and 2
  • C
    none of these
  • D
    – 2, 0 and 2
    Correct
4
If one zero of the polynomial \(p(x) = (k + 4){x^2} + 13x + 3k\) is reciprocal of the other, then the value of ‘k’ is
  • A
    3
  • B
    5
  • C
    2
    Correct
  • D
    4
5
The sum of two zeroes of the polynomial \(f(x) = 2{x^2} + (p + 3)x + 5\) is zero, then the value of ‘p’ is
  • A
    – 3
    Correct
  • B
    3
  • C
    4
  • D
    – 4
6
If ‘α’ and ‘β’ are the zeroes of a quadratic polynomial \(a{x^2} + bx + c\), then \(\alpha {\text{ }} + {\text{ }}\beta {\text{ }} = \)
  • A
    \(\frac{{ - c}}{a}\)
  • B
    \(\frac{c}{a}\)
  • C
    \(\frac{b}{a}\)
  • D
    \(\frac{{ - b}}{a}\)
    Correct
7
If ‘α’ and ‘β’ are the zeroes of a quadratic polynomial \(a{x^2} + bx + c\), then α β =
  • A
    \(\frac{{ - c}}{a}\)
  • B
    \(\frac{b}{a}\)
  • C
    \(\frac{c}{a}\)
    Correct
  • D
    \(\frac{{ - b}}{a}\)
8
The zeroes of the quadratic polynomial \({x^2} + 9x + 20\) are
  • A
    4 and 5
  • B
    – 4 and – 5
    Correct
  • C
    4 and – 5
  • D
    – 4 and 5
9
A polynomial whose sum and product of zeroes are – 4 and 3 is
  • A
    \({x^2} + 4x + 3\)
    Correct
  • B
    \({x^2} - 4x - 3\)
  • C
    none of these
  • D
    \({x^2} - 4x + 3\)
10
A quadratic polynomial with zeroes \(\frac{1}{4}\) and – 1 is
  • A
    \(4{x^2} - 3x - 1\)
  • B
    \(4{x^2} - 3x + 1\)
  • C
    \(4{x^2} + 3x + 1\)
  • D
    \(4{x^2} + 3x - 1\)
    Correct
11
A real number ‘k’ is said to be a zero of a polynomial p(x), if p(k) =
  • A
    2
  • B
    1
  • C
    0
    Correct
  • D
    3
12
If ‘α’, ‘β’ and ‘γ’ are the zeroes of a cubic polynomial \(a{x^3} + b{x^2} + cx + d\), then α + β + γ =
  • A
    \(\frac{b}{a}\)
  • B
    \(\frac{{ - c}}{a}\)
  • C
    \(\frac{{ - b}}{a}\)
    Correct
  • D
    \(\frac{c}{a}\)
13
If ‘α’, ‘β’ and ‘γ’ are the zeroes of a cubic polynomial \(a{x^3} + b{x^2} + cx + d\), then αβ + βγ + γα =
  • A
    \(\frac{c}{a}\)
    Correct
  • B
    \(\frac{b}{a}\)
  • C
    \(\frac{{ - b}}{a}\)
  • D
    \(\frac{{ - c}}{a}\)
14
If ‘α’, ‘β’ and ‘γ’ are the zeroes of a cubic polynomial \(a{x^3} + b{x^2} + cx + d\), then α βγ =
  • A
    \(\frac{{ - c}}{a}\)
  • B
    \(\frac{b}{a}\)
  • C
    \(\frac{d}{a}\)
  • D
    \(\frac{{ - d}}{a}\)
    Correct
15
The zero of the polynomial p(x) = ax + b is
  • A
    \(\frac{{ - b}}{a}\)
    Correct
  • B
    \(\frac{b}{a}\)
  • C
    \(\frac{{ - a}}{b}\)
  • D
    \(\frac{a}{b}\)