Polynomials Test

Polynomials

This is Polynomials Test-03 for CBSE class 10 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
The sum and product of the zeroes of the polynomial \({x^2} - 6x + 8\) are respectively
  • A
    \(\frac{{ - 3}}{2}\) and 1
  • B
    \(6\) and \(8\)
    Correct
  • C
    \(\frac{{ - 3}}{2}\) and – 1
  • D
    \(\frac{3}{2}\) and 1
2
If one of the zeroes of the cubic polynomial \({x^3} - 7x + 6\) is 2, then the product of the other two zeroes is
  • A
    – 3
    Correct
  • B
    3
  • C
    2
  • D
    – 2
3
If the sum of the zeroes of the cubic polynomial \(4{x^3} - k{x^2} - 8x - 12\) is \(\frac{{ - 3}}{4}\), then the value of ‘k’ is
  • A
    \(\frac{{ - 1}}{3}\)
  • B
    3
  • C
    \(\frac{1}{3}\)
  • D
    – 3
    Correct
4
If ‘2’ is the zero of both the polynomials \(3{x^2} + mx - 14\) and \(2{x^3} + n{x^2} + x - 2\), then the value of m – 2n is
  • A
    5
  • B
    – 9
  • C
    – 1
  • D
    9
    Correct
5
A quadratic polynomial whose product and sum of zeroes are \(\frac{1}{3}\) and \(\sqrt 2 \) respectively is
  • A
    \(3{x^2} + 3\sqrt 2 x + 1\)
  • B
    \(3{x^2} - 3\sqrt 2 x + 1\)
    Correct
  • C
    \(3{x^2} + x - 3\sqrt 2 \)
  • D
    \(3{x^2} - x + 3\sqrt 2 \)
6
If ‘\(\alpha \)’ and ‘\(\beta \) are the zeroes of the polynomial \(a{x^2} + bx + c\), then the value of \(\frac{1}{\alpha } + \frac{1}{\beta }\) is
  • A
    none of these
  • B
    \(\frac{c}{a}\)
  • C
    \(\frac{b}{a}\)
  • D
    \(\frac{{ - b}}{c}\)
    Correct
7
If ‘\(\alpha \)’ and ‘\(\beta \)’ are the zeroes of the polynomial \(a{x^2} + bx + c\), then the value of \(\frac{\alpha }{\beta } + \frac{\beta }{\alpha }\) is
  • A
    \(\frac{{{c^2}}}{{ab}}\)
  • B
    \(\frac{{{b^2} - 2ac}}{{ac}}\)
    Correct
  • C
    none of these
  • D
    \(\frac{{{a^2}}}{{bc}}\)
8
The polynomial \(9{x^2} + 6x + 4\) has
  • A
    no real zeroes
    Correct
  • B
    one real zero
  • C
    two real zeroes
  • D
    many real zeroes
9
If 2, – 7 and – 14 are the sum, sum of the product of its zeroes taken two at a time and the product of its zeroes of a cubic polynomial, then the cubic polynomial is
  • A
    \({x^3} - 2{x^2} + 7x + 14\)
  • B
    \({x^3} - 2{x^2} - 7x - 14\)
  • C
    \({x^3} + 2{x^2} + 7x + 14\)
  • D
    \({x^3} - 2{x^2} - 7x + 14\)
    Correct
10
The zeroes of the polynomial are \({x^3} - 2{x^2} - x + 2\)
  • A
    1, 2 and – 1
    Correct
  • B
    none of these
  • C
    1, – 2 and – 1
  • D
    1, – 2 and 1
11
The number polynomials having zeroes as – 2 and 5 is
  • A
    1
  • B
    3
  • C
    more than 3
    Correct
  • D
    2
12
Given that one of the zeroes of the cubic polynomial \(a{x^3} + b{x^2} + cx + d\) is zero, then the product of the other two zeroes is
  • A
    \(\frac{b}{a}\)
  • B
    \(\frac{c}{a}\)
    Correct
  • C
    \(\frac{{ - c}}{a}\)
  • D
    \(\frac{{ - b}}{a}\)
13
If one of the zeroes of the cubic polynomial \({x^3} + a{x^2} + bx + c\) is – 1, then the product of the other two zeroes is
  • A
    \(b - a + 1\)
    Correct
  • B
    \(b + a - 1\)
  • C
    \(b + a + 1\)
  • D
    \(b - a - 1\)
14
The number of zeroes that the polynomial f(x) = (x – 2)2 + 4 can have is
  • A
    0
  • B
    1
  • C
    2
    Correct
  • D
    3
15
Given that one of the zeroes of the quadratic polynomial \(a{x^2} + bx + c\) is zero, then the other zero is
  • A
    \(\frac{{ - c}}{a}\)
  • B
    \(\frac{{ - b}}{a}\)
    Correct
  • C
    \(\frac{b}{a}\)
  • D
    \(\frac{c}{a}\)