MCQ Questions for Class 9 Maths Polynomials Quiz 3

A term of the expression having no literal factors is called a constant term.

0%
True
0%
False
0%
Ambiguous
0%
Data insufficient

Substituting

$x= -3$ in

$x^2-5x + 4$

0%
$-2$
0%
$28$
0%
$2$
0%
$-1$

Explanation

For

$x=-3$

$x^2-5x+4$

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

$=9+15+4$

$=28 \neq R.H.S$
The correct statement is

$x^2+5x+4=28$

Substituting

$x = -3$ in

$x^2+5x$

0%
$x^2+5x$ = -24
0%
$x^2+5x$ = -30
0%
$x^2+5x$ = -10
0%
$x^2+5x$ = -6

Explanation

For

$x=-3$

$x^2+5x$

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

$=9-15$

$=-6$
The correct statement is

$x^2+5x=-6$

$(a + b)^2-(a -b)^2$ will be equal to

$2ab$ :

0%
True
0%
False
0%
Ambiguous
0%
Data insufficient

Explanation

$(a+b)^2 -(a-b)^2=(a^2+2ab+b^2)-(a^2-2ab+b^2)$

$=a^2+2ab+b^2-a^2+2ab-b^2$

$=4ab$ .

Hence, answer is

$4ab$ but not

$2ab$ .

Option

$B$ is correct.

State true or false:

$x = 2$ is a root of

$2x^3+x^2-7x-6$ .

0%
True
0%
False

Explanation

$p(x) = 2x^3+ x^2-7x-6.$

Then,

$p(2)=2(2)^3+(2)^2-7(2)-6 = 16+4-14-6=0$ .

Hence,

$x = 2$ is a root of

$p(x)$ .

Therefore, it is true and option

$A$ is correct.

Simplify

$a (a^2 + a + 1) + 5$ and find its value for a = 1

0%
6
0%
5
0%
8
0%
7

Explanation

$a (a^2 + a + 1) + 5$

$=a^3+a^2+a+5$
At

$a=1$

$=1^3+1^2+1+5$

$=1+1+1+5$

$=8$

The degree of a polynomial

$x^{3} - 27$ is

0%
$3$
0%
$1$
0%
$26$
0%
$27$

Explanation

The highest power of the variable

$x$ in the given polynomial is

$3$ .

Hence, its degree is

$3$ .

The degree of the polynomial

$4x^{2} + 3x - 7$ is:

0%
$1$
0%
$3$
0%
$7$
0%
$2$

Explanation

The highest power of the variable

$x$ in the given polynomial is

$2$ .

Hence, its degree is

$2$ .

The degree of the polynomial

$2x^{4} - 3x^{2} + 9$ is

0%
$2$
0%
$3$
0%
$4$
0%
None of the above

Explanation

The highest power of the variable

$x$ in the given polynomial is

$4$ .

Hence, its degree is

$4$ .

In a polynomial, the exponents of the variables are always

0%
integers
0%
positive integers
0%
non-negative integers
0%
non-positive integers

The degree of a polynomial

$2x^{5} - 5x^{3} - 10x + 9$ is

0%
$5$
0%
$3$
0%
$1$
0%
$9$

Explanation

Given polynomial is

$2x^5-5x^3-10x+9$ .

We know that, the degree of a polynomial is the highest power of the variable.

The highest power of the variable

$x$ in the given polynomial is

$5$ .

Hence, the degree of the given polynomial is

$5$ .

The value of the polynomial

$z^3+2z^2+5z+1$

0%
is equal when $z=1$ and $z=-1$
0%
is equal when $z=1$ and $z=0$
0%
is equal when $z=-1$ and $z=0$
0%
None of the above

Explanation

Let

$f(z) = z^3+2z^2+5z+1$

$z = 0$ value of the given polynomial =

$f(0) = 1$

Similarly,

$f(1) = 9$ &

$f(-1) = -3$

None of the three values are equal.

What is the output of

$x^2+3x+5$ , where

$x = 3?$

0%
$21$
0%
$22$
0%
$23$
0%
None of the above

Explanation

Given that:

$x^2 + 3x + 5 :$

Substituting,

$x = 3 \:we\: get ,$

$(3)^2 + 3\times 3 + 5 = 9+9+5 = 23$

$\therefore x^2 + 3x +5$ is

$23$

Given

${y= 3 ^x}$ , evaluate

$y$ when

$x=3$

0%
$3$
0%
$9$
0%
$27$
0%
$81$

Explanation

We have,

$y=3^x$
At

$x=3$

$y =3^3=3\times 3\times 3=27$
Hence, option C is correct choice.

The degree of a polynomial

$7x^{4} + 6x^{2} + x$ is

0%
$7$
0%
$2$
0%
$4$
0%
$1$

Explanation

The highest power of the variable

$x$ in the given polynomial is

$4$ .

Hence, its degree is

$4$ .

The value of a polynomial

0%
changes with the change in variable
0%
doesn"t change with the change in variable
0%
many or may not change with the change in variable
0%
all of the above

Identify zero polynomial among the following.

0%
$0$
0%
$x$
0%
$x^2$
0%
None of the above

Explanation

Consider the polynomial,

$p(x) = ax^2 + bx +c$ , if

$a=b=c= 0$ then the expression becomes zero polynomial.

Therefore, the constant polynomial whose coefficients are all equal to

$0$ is called a zero polynomial.

Hence, zero polynomial can be written as

$p(x) = 0$ .

The highest power in the polynomial

$x^2+6x+5$

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

Explanation

The highest power in the polynomial

$x^2+6x+5$ is 2.
Always check the highest exponential term of the polynomial.

Find the degree of the polynomial

$5t+\sqrt{7}$ .

0%
$5$
0%
$1$
0%
$\dfrac{1}{2}$
0%
None of the above

Explanation

The given polynomial is

$5t+\sqrt{7}$

The degree is the highest power of the variable in the polynomial.

Hence, the degree of the given polynomial is

$1$ .

The zero of the linear polynomial

$x+5$ is:

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

Explanation

$zero$ or root of a

$polynomial$ function is a number that, when plugged in for the variable, makes the function equal to

$zero.$

Hence lets by substituting

$x= -5$ we get

Equation :

$x + 5 = -5 + 5 = 0$ .

$\therefore$ zero of the linear polynomial

$x + 5$ is

$- 5$ .

Therefore, option

$B$ is correct.

$x=-1$ a solution of

$\displaystyle { x }^{ 2 }+x+1=0$ ?

0%
Yes
0%
No
0%
Can't say
0%
None

Explanation

Put

$x=-1$ in equation

$\displaystyle { x }^{ 2 }+x+1=0$ .

$\displaystyle f(-1)= { \left( -1 \right) }^{ 2 }+\left( -1 \right) +1$

$\displaystyle =1-1+1\ne0$ .

$\displaystyle \therefore \quad x=-1$ is not a solution of

$\displaystyle { x }^{ 2 }+x+1=0$ .

Therefore, option

$B$ is correct.

Identify the zero polynomial from the following.

0%
$0$
0%
$5$
0%
$4$
0%
$3$

Explanation

The degree of the zero polynomial is undefined.
Example:

$p(x) = ax^2+bx+c$ , when the constants

$a = b = c = 0$ is considered as zero polynomial.

Find the degree of

$2-y^2-y^3+2y^8$

0%
$2$
0%
$-1$
0%
$3$
0%
$8$

Explanation

Put the polynomial

$2-y^2-y^3+2y^8$ in standard form. The term with the highest exponent should be first, and the term with the lowest exponent should be last. This will help us see which term has the exponent with the largest value. Therefore, the standard form is:

$2y^8-y^3-y^2+2$

The power is simply number in the exponent. In the polynomial,

$2y^8-y^3-y^2+2$ , the power of the first term is

$8$ which is the largest exponent of

$y$ and hence it is the degree of given polynomial.

Find the degree of the polynomial

$x^3+x+2$ .

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

Explanation

The degree of the polynomial

$x^3+x+2$ is

$3$ .

Find the degree of the polynomial

$4-y^2$ .

0%
$4$
0%
$-1$
0%
$2$
0%
None of the above

Explanation

The

$degree$ of a

$polynomial$ is the highest degree of its

$terms$

Here

$y^2$ has degree of

$2$ .

Hence, the degree of the polynomial

$4-y^2$ is

$2$

A linear polynomial has _____ zero(s).

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

Explanation

Consider the polynomial,

$p(x) = bx +c$ .

Here, since the highest power of

$x$ is

$1$ ,

the degree of the given polynomial is

$1$ , i.e. the given polynomial is a linear polynomial.

To find the zero of a polynomial, we write

$p(x) = 0$ .

That is,

$bx +c=0$

$\implies$

$bx =-c$

$\implies$

$x =\dfrac{-c}{b}$

$\implies$

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

That is, a linear polynomial can have one and only one zero.

Therefore, option

$A$ is correct.

Find roots of equation

$\displaystyle { a }^{ 4 }{ x }^{ 2 }-{ b }^{ 4 }=0$

0%
$\displaystyle { { b }^{ 2 } }/{ { a }^{ 2 } },-{ { b }^{ 2 } }/{ { a }^{ 2 } }$
0%
$\displaystyle { { b }^{ 2 } }/{ { a }^{ 2 } },{ { b }^{ 2 } }/{ { a }^{ 2 } }$
0%
$\displaystyle { { a }^{ 2 } }/{ { { b }^{ 2 } } },\frac { { a }^{ 2 } }{ { { b }^{ 2 } } }$
0%
$\displaystyle { { a }^{ 2 } }/{ { { b }^{ 2 } } },-\frac { { a }^{ 2 } }{ { { b }^{ 2 } } }$

Explanation

$\displaystyle { a }^{ 4 }{ x }^{ 2 }-{ b }^{ 4 }=0$

Since,

$(a^2-b^2)=(a-b)(a+b)$

$\displaystyle \left( { a }^{ 2 }x+{ b }^{ 2 } \right) \left( { a }^{ 2 }x-{ b }^{ 2 } \right) =0,{ a }^{ 2 }x={ b }^{ 2 }and \ ,{ a }^{ 2 }x=-{ b }^{ 2 }$

$\displaystyle x={ { b }^{ 2 } }/{ { a }^{ 2 } },x=-{ { b }^{ 2 } }/{ { a }^{ 2 } }$

$p(x) = \dfrac{37}{15}$ is a _______ polynomial.

0%
linear
0%
quadratic
0%
cubic
0%
none of these

Explanation

The general form of a constant polynomial is

$p(x)=c$ with constant

$c$ .

Since

$p(x)=\frac { 37 }{ 15 }$ is a polynomial with constant term

$\frac { 37 }{ 15 }$ and there is no variable in it.

Hence,

$p(x)=\frac { 37 }{ 15 }$ is a constant polynomial.

$\displaystyle x=-10$ is a solution of

$\displaystyle { x }^{ 2 }+5x-9=0$ ?

0%
Yes
0%
No
0%
None
0%
Can't say

Explanation

Put

$\displaystyle x=-10$ in equation

$\displaystyle { x }^{ 2 }+5x-9=0$ .

$\displaystyle { \left( -10 \right) }^{ 2 }+5\left( -10 \right) -9=100-50-9$

$\displaystyle =\quad 100-59=41\neq 0$ .

$\displaystyle \therefore$ The equation does not have

$x=-10$ , solution.

Therefore, option

$B$ is correct.

$\displaystyle x=\dfrac { 5 }{ 2 }$ a solution of

$\displaystyle \left( 6x+16 \right) \left( 4x+10 \right) =0$ ?

0%
Yes
0%
No
0%
Can't say
0%
None

Explanation

Put

$\displaystyle x=\dfrac { 5 }{ 2 }$ in equation

$\displaystyle \left( 6x+16 \right) \left( 4x+10 \right) =0$

$\displaystyle \left( 6\times \frac { 5 }{ 2 } +16 \right) \left( 4\times \frac { 5 }{ 2 } +10 \right) =\left( \frac { 30 }{ 2 } +16 \right) \left( \frac { 20 }{ 2 } +10 \right)$

$\displaystyle =\left( 15+16 \right) \left( 10+10 \right)$

$\displaystyle =\left( 31 \right) \left( 20 \right) \neq 0$

$\displaystyle \therefore \quad x=\frac { 5 }{ 2 }$ is not a solution of equation

$\displaystyle \left( 6x+16 \right) \left( 4x+10 \right)$

Therefore, option

$B$ is correct.

CBSE Questions for Class 9 Maths Polynomials Quiz 3 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

CBSE Questions for Class 9 Maths Polynomials Quiz 3 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

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