Polynomials Test

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Polynomials Test - 16

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Weekly Quiz Competition

Question 1
1 / -0

Degree of the polynomial $$4x^4 + 5x + 7$$, is

A
4

B
5

C
2

D
7

Solution

Given polynomial is $$4x^4 + 5x + 7$$
The highest power of $$x$$ having a non zero coefficient is 4.
Hence, the degree is 4.
Question 2
1 / -0

The degree of the polynomial $$p(x) = x^{3}-9x+3x^{5}$$ is

A
$$3$$

B
$$0$$

C
$$5$$

D
$$2$$

Solution

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 $$5$$.
Question 3
1 / -0

The degree of the polynomials $$p(y) = y^{3}, q(y) = (1-y^{4})$$ are

A
$$7,0$$

B
$$0,4$$

C
$$3,4$$

D
$$4,1$$
Question 4
1 / -0

Find the zeroes of the polynomial in the following :
$$p(x) = x - 4$$.

A
$$4$$

B
$$3$$

C
$$-4$$

D
$$0$$

Solution

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.
Question 5
1 / -0

The degree of the polynomial $$2x-1$$ is

A
$$0$$

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

C
$$-1$$

D
$$1$$

Solution

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 $$= 1$$
Question 6
1 / -0

$$3 $$ is a type of

A
Linear Polynomial

B
Constant Polynomial

C
Cubic Polynomial

D
Quadratic Polynomial

Solution

$$3$$ is a constant term as it is independent of any variable.
Therefore, it is a constant polynomial.
Question 7
1 / -0

Degree of the polynomial $$p(x) = -10$$ is:

A
$$-10$$

B
$$10$$

C
$$0$$

D
$$1$$

Solution

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 $$= 0$$
Question 8
1 / -0

$$\sqrt 2$$ is a polynomial of degree

A
$$2$$

B
$$0$$

C
$$1$$

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

Solution

We can write it as $$\sqrt2 = \sqrt2 \times x^0$$
Thus, degree is 0.
Question 9
1 / -0

Which is a binomial of degree $$20$$?

A
$$x^{20}+1$$

B
$$x^{19}+1$$

C
$$20x+1$$

D
$$20xy+1$$

Solution

$${ x }^{ 20 } +1$$
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 $$20$$.
Question 10
1 / -0

The zeroes of the polynomial $$p(x)=(x-6) (x-5)$$ are :

A
-6, -5

B
-6, 5

C
6, -5

D
6, 5

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, $$p(x)=0$$.
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.

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Re-Attempt Weekly Quiz Competition

Polynomials Test - 16

Result

Polynomials Test - 16

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Question 1

4

5

2

7

Solution

Question 2

$$3$$

$$0$$

$$5$$

$$2$$

Solution

Question 3

$$7,0$$

$$0,4$$

$$3,4$$

$$4,1$$

Question 4

$$4$$

$$3$$

$$-4$$

$$0$$

Solution

Question 5

$$0$$

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

$$-1$$

$$1$$

Solution

Question 6

Linear Polynomial

Constant Polynomial

Cubic Polynomial

Quadratic Polynomial

Solution

Question 7

$$-10$$

$$10$$

$$0$$

$$1$$

Solution

Question 8

$$2$$

$$0$$

$$1$$

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

Solution

Question 9

$$x^{20}+1$$

$$x^{19}+1$$

$$20x+1$$

$$20xy+1$$

Solution

Question 10

-6, -5

-6, 5

6, -5

6, 5

Solution

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