MCQ Questions for Class 9 Maths Polynomials Quiz 1

The degree of the polynomial

$2x-1$ is

0%
$0$
0%
$\dfrac{1}{2}$
0%
$-1$
0%
$1$

Explanation

For a polynomial the degree is the value of highest power of the variable.
For

$2x-1$
Highest power of variable

$x$ is

$1$

$\therefore$ Degree

$= 1$

State true or false:

$3$ is a zero of

$x+3$ .

0%
True
0%
False

Explanation

Let

$f(x)=x+3$ .

$3$ is zero of

$f(x)$ ,
then

$f(3)$ must be equal to

$0$ .

But,

$f(3)=(3)+3$

$=6$ .
Hence, the statement is false.

Therefore, option

$B$ is correct.

The degree of the polynomial

$p(x) = x^{3}-9x+3x^{5}$ is

0%
$3$
0%
$0$
0%
$5$
0%
$2$

Explanation

Given polynomial is

$p(x) = x^{3}-9x+3x^{5}$ .

We know that, the degree of a polynomial is the highest power of any of its variables.

Here, in

$p(x) = x^{3}-9x+3x^{5}$ ,the highest power of variable

$x$ is

$5$ .

So, the degree is

$5$ .

Hence, the degree of

$p(x) = x^{3}-9x+3x^{5}$ is

$5$ .

The degree of the polynomials

$p(y) = y^{3}, q(y) = (1-y^{4})$ are

0%
$7,0$
0%
$0,4$
0%
$3,4$
0%
$4,1$

Find the zeroes of the polynomial in the following :

$p(x) = x - 4$ .

0%
$4$
0%
$3$
0%
$-4$
0%
$0$

Explanation

Zero of

$p(x)=x-4$ will be when,

$p(x)=0$ .

$=>x-4=0$

$=>x=4$ .
Thus,

$4$ is the zero of the polynomial.

Hence, option

$A$ is correct.

$\sqrt 2$ is a polynomial of degree

0%
$2$
0%
$0$
0%
$1$
0%
$\dfrac {1}{2}$

Explanation

We can write it as

$\sqrt2 = \sqrt2 \times x^0$
Thus, degree is 0.

$3$ is a type of

0%
Linear Polynomial
0%
Constant Polynomial
0%
Cubic Polynomial
0%
Quadratic Polynomial

Explanation

$3$ is a constant term as it is independent of any variable.

Therefore, it is a constant polynomial.

Degree of the polynomial

$p(x) = -10$ is:

0%
$-10$
0%
$10$
0%
$0$
0%
$1$

Explanation

Degree of a polynomial is the value of highest power of any variable.
For

$p(x) = -10$
There is no variable in the equation.

So, highest degree of variable is zero.

$\therefore$ Degree

$= 0$

Which is a binomial of degree

$20$ ?

0%
$x^{20}+1$
0%
$x^{19}+1$
0%
$20x+1$
0%
$20xy+1$

Explanation

${ x }^{ 20 } +1$
If an expression contains two unlike terms, then it is called as a binomial.
For binomial of degree

$20,$ the highest power of variable should be

$20$ .

If the degree of polynomial

$p(y)$ is

$a$ , then the maximum number of zeroes of

$p(y$ ) would be:

0%
$a+1$
0%
$a-1$
0%
$a$
0%
$2a$

Explanation

We know, the number of zeroes of a polynomial is equal to or less than the degree of the polynomial.
Hence, if the degree of the polynomial is

$a$ , then the number of zeros it can have is

$a,a-1,a-2,.......0$ , i.e. it can have

$a$ number of zeros.

Hence, the maximum number of zeroes is

$a$ .

Therefore, option

$C$ is correct.

Degree of which of the following polynomials is zero?

0%
$x$
0%
$15$
0%
$y$
0%
$x+x^2$

Explanation

The degree of a polynomial is the highest degree of its monomials (individual terms) with non-zero coefficients.

For, non-zero constants, degree is zero.

Here,

$15$ is the only non-zero constant and thus has zero degree.

Hence,

$B$ is correct.

The zeroes of the polynomial

$p(x)=(x-6) (x-5)$ are :

0%
-6, -5
0%
-6, 5
0%
6, -5
0%
6, 5

Explanation

To find the zeroes of the polynomial, means to find those values of

$x$ for which the value of equation is zero.

That is,

$p(x)=0$ .

Then,

$p(x)=\left( x-6 \right) \left( x-5 \right) =0$ .

Hence,

$x-6=0 , x=6$ or

$x-5=0,x=5$ .

That is, the zeros are

$6$ and

$5$ .

Hence, option

$D$ is correct.

Which of the following polynomials has -

$3$ as a zero ?

0%
$x-3$
0%
$x^2-9$
0%
$x^2-3x$
0%
$x^2+3$

Explanation

$-3$ is a zero, then

$f(-3)=0$ ...(where

$f$ is the function)

$(A)$ ,

$f(-3) = -3-3 = -6$

$(B)$ ,

$f(-3) = (-3)^2-9 = 9-9 = 0$

$(C)$ ,

$f(-3) = (-3)^2-3(-3) = 9+9 = 18$

$(D)$ ,

$f(-3) = (-3)^2+3 = 12$

Hence, option

$B$ is correct.

Zero of the polynomial

$p(x)$ where

$p(x) = ax, a \neq 0$ is :

0%
1
0%
a
0%
0
0%
$\frac{1}{a}$

Explanation

Zeroes of the polynomial is the value of the variable for which the polynomial becomes

$0$ i.e.

$p(x)=0$ .

Here,

$p(x)=ax$ .

Putting

$p(x)=0$ , we get,

$ax=0$

or,

$x=0$

$\left( \because a\neq 0 \right)$

So, option

$C$ is correct.

Zero of the polynomial

$p (x) = cx + d$ is :

0%
$-d$
0%
$-c$
0%
$\dfrac{d}{c}$
0%
$- \dfrac{d}{c}$

Explanation

Zeroes of the polynomial is the value of the variable for which the polynomial becomes

$0$ , i.e.

$p(x)=0$ .

Here,

$p(x)=cx+d$ .

Putting

$p(x)=0$ , we get,

$cx+d=0$

or,

$x=\dfrac{-d}{c}$ .

Therefore, option

$D$ is correct.

Substitute

$x = 3$ and find the value of the given expression

$x^2 -5x + 4$

0%
$-2$
0%
$5$
0%
$-4$
0%
$0$

Explanation

Given

$\ x=3$
Putting the value of

$x$ , we get,

$x^{ 2 }-5x+4$

$=(3)^2-5(3)+4$

$=9-15+4$

$=13-15$

$=-2$

Find the zeros of the polynomial

$3\pi x - 4$ :

0%
$\dfrac{4}{3\pi}$
0%
$\dfrac{3\pi}{4}$
0%
$\dfrac{4\pi}{3}$
0%
$0$

Explanation

To find the zeroes of the polynomial means to find those values of

$x$ for which the value of equation is zero.

That is,

$p(x)=0$ , where

$3\pi x-4=0$ .

$3\pi x=4$

$\implies$

$x=\cfrac { 4 }{ 3\pi }$ .

Hence, option

$A$ is correct.

If the degree of polynomial

$p(x)$ is

$a$ , then the number of zeroes of

$p(x)$ would be :

0%
$a+1$
0%
$a-1$
0%
$a$
0%
$2a$

Explanation

For a polynomial of degree

$a$ , the number of roots (zeros) is

$a$ .

Let a general polynomial of degree

$n$ be

$p(x)= a^{}_{n}x^n+a{}_{n-1}x^{n-1}+........+a{}_{0}$

Here, this polynomial has

$n$ roots (zeros), which can be real, imaginary or both depending on the polynomial.

That is, a polynomial of degree

$a$ has

$a$ zeroes.

Therefore, option

$C$ is correct.

The zero of the polynomial

$p(x) = 2x + 5$ is :

0%
$\dfrac{2}{5}$
0%
$\dfrac{5}{2}$
0%
$0$
0%
$- \dfrac{5}{2}$

Explanation

Zero of a polynomial is the value of the variable for which the polynomial becomes

$0$ .

Now,

$p(x)=2x+5$ .

For,

$p(x)=0$ ,

$2x+5=0$ .

or,

$x=\dfrac{-5}{2}$ .

Therefore, option

$D$ is correct.

The degree of the polynomial

$2 - y^{2} - y^{3} + 2y^{7}$ is :

0%
2
0%
7
0%
0
0%
3

Explanation

The degree of a polynomial is the highest degree of its monomials (individual terms) with non-zero coefficients. The degree of a term is the sum of the exponents of the variables that appear in it, and thus is a non-negative integer.

Hence, for

$2-y^2-y^3+2y^7$ , the degree

$=7$

So, answer is

$B$ .

0%
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
0%
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
0%
Assertion is correct but Reason is incorrect
0%
Assertion is incorrect but Reason is correct

Explanation

We know that,
The constant polynomial

$0$ is called a zero polynomial.
The degree of a zero polynomial is not defined.

$\therefore$ Assertion is true.
The degree of a non-zero constant polynomial is zero.

$\therefore$ Reason is true.
Since both Assertion and Reason are true and Reason is not a correct explanation of Assertion.
The correct answer is B.

State true or false:

A polynomial cannot have more than one zero.

0%
True
0%
False

Explanation

A polynomial can have any number of zeroes. It depends upon the degree of the polynomial. In general, a polynomial of degree '

$n$ ' can have '

$n$ ' zeroes.

Therefore, the given statement is false and option

$B$ is correct.

Degree of a constant polynomial is

0%
$1$
0%
$0$
0%
$2$
0%
not defined

Explanation

$\textbf{Step -1: Define constant polynomial.}$

$\text{A polynomial having no variables and only constant values is called a constant polynomial.}$

$\text{For example.- }f(x) = 8, g(k) = -10$

$\therefore \text{A constant polynomial has its highest degree as 0.}$

$\textbf{Hence, degree of constant polynomial is 0. (Option B)}$

A cubic polynomial is a polynomial with degree :

0%
1
0%
3
0%
0
0%
2

Explanation

A cubic polynomial is a polynomial of degree 3, or in simplier terms highest power of x is 3,

It of the form

$f(x)=a{ x }^{ 3 }+b{ x }^{ 2 }+cx+d$ where a,b,c,d belongs to real numbers.

Hence correct option is B.

The zeroes of the polynomial

$p(x)=(x-6) (x-5)$ are :

0%
$-6, -5$
0%
$-6, 5$
0%
$6, -5$
0%
$6, 5$

Explanation

To find the zeroes of the polynomial means to find those values of x for which the value of equation is zero.

$p(x)=0$ .

$p(x)=\left( x-6 \right) \left( x-5 \right)$ =0

hence

$x-6=0 , x=6$ OR

$x-5=0,x=5$ .

Therefore, option

$D$ is correct.

A polynomial of degree

$n$ can have at most

$n$ zeros.

0%
True
0%
False

Explanation

A polynomial of degree n has at most n zeros' so given statement is true.

That is, option

$A$ is correct.

A quadratic polynomial can have at most

$2$ zeroes and a cubic polynomial can have at most ........ zeroes.

0%
$3$
0%
$2$
0%
$1$
0%
None of the above

Explanation

'The maximum number of possible roots (zeros) of a polynomial is equal to its degree, so cubic polynomial has at most 3 roots (zeros).

Therefore, option

$A$ is correct.

Zero of the polynomial

$3 \pi x-4$ is :

0%
$\dfrac{4}{3\pi}$
0%
$\dfrac{3\pi}{4}$
0%
$\dfrac{4\pi}{3}$
0%
$0$

Explanation

Zero of a polynomial is the value of the variable for which the polynomial becomes

$zero$ .

So, for

$3\pi x-4=0$

$\implies$

$x=\dfrac {4}{3\pi}$ , is the required zero.

Hence,

$A$ is correct.

What is the degree of the following polynomial expression:

$4x^{2} - 3x + 2$

0%
$1$
0%
$2$
0%
$3$
0%
$4$

Explanation

The degree of the polynomial is equal to the highest power of the variable present in the expression. Here,

$x$ is the variable and its highest power is

$2$ in the term

$4x^2$ . Hence, the degree of the polynomial is equal to

$2.$

Use the identity

$(a+b)(a-b) = a^2-b^2$ to evaluate:

$33\times 27$ .

0%
$891$
0%
$881$
0%
$981$
0%
$841$

Explanation

We know,

$33 \times 27 = (30 + 3) \times (30 - 3)$ .

Applying the formula

$(a+b)(a-b) = { a }^{ 2 }-{ b }^{ 2 }$ , where

$a = 30 , b = 3$ ,

we get,

$33 \times 27 = (30 + 3) \times (30 - 3) = { 30 }^{ 2 }-{ 3 }^{ 2 } = 900 - 9 = 891$ .

Therefore, option

$A$ is correct.

CBSE Questions for Class 9 Maths Polynomials Quiz 1 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

CBSE Questions for Class 9 Maths Polynomials Quiz 1 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

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