Polynomials Test

Result

Polynomials Test - 17

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

Which of the following polynomials has -$$3$$ as a zero ?

A
$$x-3$$

B
$$x^2-9$$

C
$$x^2-3x$$

D
$$x^2+3$$

Solution

If $$-3$$ is a zero, then $$f(-3)=0$$ ...(where $$f$$ is the function)
In $$(A)$$, $$f(-3) = -3-3 = -6$$
In $$(B)$$, $$f(-3) = (-3)^2-9 = 9-9 = 0$$
In $$(C)$$, $$f(-3) = (-3)^2-3(-3) = 9+9 = 18$$
In $$(D)$$,$$f(-3) = (-3)^2+3 = 12$$
Hence, option $$B$$ is correct.
Question 2
1 / -0

Zero of the polynomial $$p(x)$$ where $$p(x) = ax, a \neq 0$$ is :

A
1

B
a

C
0

D
$$\frac{1}{a}$$

Solution

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.
Question 3
1 / -0

Degree of which of the following polynomials is zero?

A
$$x$$

B
$$15$$

C
$$y$$

D
$$x+x^2$$

Solution

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.
Question 4
1 / -0

Zero of the polynomial $$p (x) = cx + d$$ is :

A
$$-d$$

B
$$-c$$

C
$$\dfrac{d}{c}$$

D
$$- \dfrac{d}{c}$$

Solution

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.
Question 5
1 / -0

Substitute $$x = 3$$ and find the value of the given expression
$$x^2 -5x + 4$$

A
$$-2$$

B
$$ 5$$

C
$$-4$$

D
$$ 0$$

Solution

Given$$\ x=3$$
Putting the value of $$x$$, we get,
$$x^{ 2 }-5x+4$$
$$=(3)^2-5(3)+4$$
$$=9-15+4$$
$$=13-15$$
$$=-2$$
Question 6
1 / -0

Find the zeros of the polynomial $$3\pi x - 4$$ :

A
$$\dfrac{4}{3\pi}$$

B
$$\dfrac{3\pi}{4}$$

C
$$\dfrac{4\pi}{3}$$

D
$$0$$

Solution

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.
Question 7
1 / -0

If the degree of polynomial $$ p(y)$$ is $$a$$, then the maximum number of zeroes of $$p(y$$) would be:

A
$$a+1$$

B
$$a-1$$

C
$$a$$

D
$$2a$$

Solution

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.
Question 8
1 / -0

The zero of the polynomial $$p(x) = 2x + 5$$ is :

A
$$\dfrac{2}{5}$$

B
$$\dfrac{5}{2}$$

C
$$0$$

D
$$- \dfrac{5}{2}$$

Solution

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.
Question 9
1 / -0

8 is a polynomial of degree :

A
1

B
$$\dfrac{1}{2}$$

C
8

D
0

Solution

Degree of a polynomial is the highest power of the variable in the polynomial.
Degree of $$8$$ is $$0$$ since $$8x^0$$$$=8$$.
Question 10
1 / -0

Degree of a constant polynomial is

A
$$1$$

B
$$0$$

C
$$2$$

D
not defined

Solution

$$\textbf{Step -1: Define constant polynomial.}$$
$$\text{A polynomial having no variables and only constant values is called a constant polynomial.}$$
$$\text{For example.- }f(x) = 8, g(k) = -10$$
$$\therefore \text{A constant polynomial has its highest degree as 0.}$$

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

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Polynomials Test - 17

Result

Polynomials Test - 17

Score

-

Rank

-

SHARING IS CARING

Question 1

$$x-3$$

$$x^2-9$$

$$x^2-3x$$

$$x^2+3$$

Solution

Question 2

1

a

0

$$\frac{1}{a}$$

Solution

Question 3

$$x$$

$$15$$

$$y$$

$$x+x^2$$

Solution

Question 4

$$-d$$

$$-c$$

$$\dfrac{d}{c}$$

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

Solution

Question 5

$$-2$$

$$ 5$$

$$-4$$

$$ 0$$

Solution

Question 6

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

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

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

$$0$$

Solution

Question 7

$$a+1$$

$$a-1$$

$$a$$

$$2a$$

Solution

Question 8

$$\dfrac{2}{5}$$

$$\dfrac{5}{2}$$

$$0$$

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

Solution

Question 9

1

$$\dfrac{1}{2}$$

8

0

Solution

Question 10

$$1$$

$$0$$

$$2$$

not defined

Solution

User

Question Analysis

My Perfomance

Score

-

Rank

-

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.