Polynomials Test

Result

Polynomials Test - 22

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

Identify zero polynomial among the following.

A
$$0$$

B
$$x$$

C
$$x^2$$

D
None of the above

Solution

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 $$p(x) = 0$$.
Question 2
1 / -0

The highest power in the polynomial $$x^2+6x+5$$

A
$$2$$

B
$$1$$

C
$$0$$

D
None of the above

Solution

The highest power in the polynomial $$x^2+6x+5$$ is 2.
Always check the highest exponential term of the polynomial.
Question 3
1 / -0

Find the degree of the polynomial $$5t+\sqrt{7}$$.

A
$$5$$

B
$$1$$

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

D
None of the above

Solution

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 $$1$$.
Question 4
1 / -0

The value of the polynomial $$z^3+2z^2+5z+1$$

A
is equal when $$z=1$$ and $$z=-1$$

B
is equal when $$z=1$$ and $$z=0$$

C
is equal when $$z=-1$$ and $$z=0$$

D
None of the above

Solution

Let $$ f(z) = z^3+2z^2+5z+1 $$
At $$ z = 0 $$ value of the given polynomial = $$ f(0) = 1 $$
Similarly, $$ f(1) = 9 $$ &
$$ f(-1) = -3 $$
None of the three values are equal.
Question 5
1 / -0

The zero of the linear polynomial $$x+5$$ is:

A
$$5$$

B
$$-5$$

C
$$4$$

D
$$-4$$

Solution

A $$zero$$ 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.
Question 6
1 / -0

Identify the zero polynomial from the following.

A
$$0$$

B
$$5$$

C
$$4$$

D
$$3$$

Solution

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.
Question 7
1 / -0

Find the degree of $$2-y^2-y^3+2y^8$$

A
$$2$$

B
$$-1$$

C
$$3$$

D
$$8$$

Solution

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.
Question 8
1 / -0

Find the degree of the polynomial $$x^3+x+2$$.

A
$$3$$

B
$$2$$

C
$$1$$

D
None of the above

Solution

The degree of the polynomial $$x^3+x+2$$ is $$3$$.
Question 9
1 / -0

Find the degree of the polynomial $$4-y^2$$.

A
$$4$$

B
$$-1$$

C
$$2$$

D
None of the above

Solution

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 $$2$$
Question 10
1 / -0

A linear polynomial has _____ zero(s).

A
$$1$$

B
$$2$$

C
$$3$$

D
$$4$$

Solution

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.

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Polynomials Test - 22

Result

Polynomials Test - 22

Score

-

Rank

-

SHARING IS CARING

Question 1

$$0$$

$$x$$

$$x^2$$

None of the above

Solution

Question 2

$$2$$

$$1$$

$$0$$

None of the above

Solution

Question 3

$$5$$

$$1$$

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

None of the above

Solution

Question 4

is equal when $$z=1$$ and $$z=-1$$

is equal when $$z=1$$ and $$z=0$$

is equal when $$z=-1$$ and $$z=0$$

None of the above

Solution

Question 5

$$5$$

$$-5$$

$$4$$

$$-4$$

Solution

Question 6

$$0$$

$$5$$

$$4$$

$$3$$

Solution

Question 7

$$2$$

$$-1$$

$$3$$

$$8$$

Solution

Question 8

$$3$$

$$2$$

$$1$$

None of the above

Solution

Question 9

$$4$$

$$-1$$

$$2$$

None of the above

Solution

Question 10

$$1$$

$$2$$

$$3$$

$$4$$

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.