Polynomials Test

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Polynomials Test - 24

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Weekly Quiz Competition

Question 1
1 / -0

What is the degree of the following polynomial expression:
$$\dfrac{4}{3}x^{7} - 3x^{5} + 2x^{3} + 1$$

A
7

B
4

C
5

D
3

Solution

Clearly, the degree of the polynomial expression $$\dfrac{4}{3}x^{7} - 3x^{5} + 2x^{3} + 1$$ is $$7$$.
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.
Question 2
1 / -0

Degree of a constant polynomial is

A
$$1$$

B
$$0$$

C
$$2$$

D
not defined

Solution

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

$$\textbf{Hence, degree of constant polynomial is 0. (Option B)}$$
Question 3
1 / -0

The polynomial, $$\sqrt{3}x^2+2x+1$$ is a _______ polynomial.

A
linear

B
quadratic

C
cubic

D
bi-quadratic

Solution

Quadratic equation is a second order polynomial with $$3$$ coefficients - $$a, b, c$$. The quadratic equation is given by: $$ax^2 + bx + c = 0$$.

Here, the polynomial $${ \sqrt { 3 } x }^{ 2 }+2x+1$$ is a second order polynomial and has three coefficients $$a=\sqrt { 3 }$$, $$b=2$$ and $$c=1$$.

Hence, the polynomial $${ \sqrt { 3 } x }^{ 2 }+2x+1$$ is a quadratic polynomial.
Question 4
1 / -0

A cubic polynomial is a polynomial with degree :

A
1

B
3

C
0

D
2

Solution

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.
Question 5
1 / -0

What is the degree of the following polynomial expression:
$$\dfrac{5}{3} x^{3} + 7x + 16$$

A
2

B
3

C
1

D
$$\dfrac{5}{3}$$

Solution

Clearly, the degree of the polynomial expression $$\frac{5}{3} x^{3} + 7x + 16$$ is $$3$$.
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.
Question 6
1 / -0

What is the degree of the following polynomial expression:
$$4x^{2} - 3x + 2$$

A
$$1$$

B
$$2$$

C
$$3$$

D
$$4$$

Solution

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 $$2.$$
Question 7
1 / -0

The given graph represents the polynomial $$p(x)$$. Find the number of zeros of the polynomial $$p(x).$$

A
$$0$$

B
$$2$$

C
$$1$$

D
$$3$$

Solution

The zeros of the polynomial are given by $$y=p(x)=0$$
This means that the zeros of the polynomial are the points on the graph where it intersects the x-axis.
Here, the graph intersects the x-axis at only one point.
Thus, the number of zeros is one.
Question 8
1 / -0

Find the degree of the following polynomial
$$x^9-x^4+x^{12}+x-2$$

A
12

B
9

C
4

D
2

Solution

The degree is the value of the greatest exponent of any expression (except the constant) in the polynomial.
Given,
$$x^9-x^4+x^{12}+x-2$$
Since there are 4 terms $$x^9-x^4+x^{12}+x-2$$, this is a polynomial and has the highest degree $$x^{12}$$ of all the terms.
Therefore,
Degree is $$12$$
Question 9
1 / -0

Find the degree of the following polynomial
$$3y+4y^2$$

A
y

B
0

C
1

D
2

Solution

We know that, the degree is the value of the greatest exponent of any expression (except the constant) in the polynomial.
Given polynomial is $$3y+4y^2$$
It is a polynomial in $$y$$ having highest exponent value as $$2$$.

Hence, the degree of the given polynomial is $$2$$.
Question 10
1 / -0

Ratio of the sum of the roots of $$x^{2}-9x+18=0$$ to the product of the roots is:

A
$$1: 2$$

B
$$2: 1$$

C
$$-1: 2$$

D
$$-2: 1$$

Solution

We know that equation $$ax^{2}+bx+c=0$$
Then sum of roots $$=\dfrac{-b}{a}$$ and product of roots$$=\dfrac{c}{a}$$
Given equation is $$x^2-9x+19=0$$
Sum of roots $$=9$$
Product of the roots $$=18$$
Therefore, the ratio of sum of roots to the product of roots is $$ 9:18$$ i,e., $$1:2$$.

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Polynomials Test - 24

Result

Polynomials Test - 24

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SHARING IS CARING

Question 1

7

4

5

3

Solution

Question 2

$$1$$

$$0$$

$$2$$

not defined

Solution

Question 3

linear

quadratic

cubic

bi-quadratic

Solution

Question 4

1

3

0

2

Solution

Question 5

2

3

1

$$\dfrac{5}{3}$$

Solution

Question 6

$$1$$

$$2$$

$$3$$

$$4$$

Solution

Question 7

$$0$$

$$2$$

$$1$$

$$3$$

Solution

Question 8

12

9

4

2

Solution

Question 9

y

0

1

2

Solution

Question 10

$$1: 2$$

$$2: 1$$

$$-1: 2$$

$$-2: 1$$

Solution

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