Polynomials Test

Result

Polynomials Test - 31

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following is a linear polynomial ?

A
$$x+{x}^{2}$$

B
$$x+1$$

C
$${5x}^{2}-x+3$$

D
$$x+\dfrac {1}{x}$$

Solution

$$\textbf{Step1: Check Every Option to Find whether it is Linear Polynomial or Not}$$
$$\text{The General form of linear polynomial is p(x)=ax+b}$$
$$\text{where x is a Variable and b is a Constant}$$
$$\text{The first term of this polynomial has power 1 and Therefore, the degree of the polynomial is 1.}$$
$$\text{Since Linear Polynomial is Polynomial in terms Single variable with degree 1}$$
$$\text{ By Verifying every option,we can say that-}$$
$$\text{Option A.}$$  $$x+x^2:$$ $$\text{It is not a Linear Polynomial since Power of x i.e. Degree is not 1}$$
$$\text{Option B.}$$   $$x+1:$$ $$\text{It is a Linear Polynomial in ax+b form with Degree 1.}$$
$$\text{Option C.}$$  $$5x^2-x+3:$$ $$\text{It is not a Linear Polynomial since Power of x i.e. Degree is not 1}$$
$$\text{Option D.}$$  $$x+x^{-1}:$$  $$\text{It is not a Linear Polynomial since Power of x is Ngeative.}$$

$$\textbf{Hence, the Expression $x+1$ is a Linear Polynomial.}$$
Question 2
1 / -0

The expression with only constant is

A
$$y + 3$$

B
$$3x$$

C
$$5(21 - 7)$$

D
$$5 - 5n$$

Solution
Question 3
1 / -0

What is the degree of the polynomials $$\sqrt 7 $$?

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

B
$$5$$

C
$$2$$

D
$$0$$

Solution
Question 4
1 / -0

The degree of the polynomial $$3x^3y-5xy^4-2x+1$$ is

A
5

B
4

C
3

D
2

Solution

The degree of the polynomial
$$3x^3y-5xy^4-2x+1$$ is of $$-5xy^4\implies1+4=5$$ [as it is the highest]
Question 5
1 / -0

If two of the zeros of the polynomial $$t^4-7t^3+70t-100$$ are same as that of $$t^2-7t+10$$, then find the other two zeros.

A
$$10$$ and $$-10$$

B
$$10$$ and $$-\sqrt{10}$$

C
$$\sqrt{10}$$ and $$-10$$

D
$$\sqrt{10}$$ and $$-\sqrt{10}$$

Solution
Question 6
1 / -0

If $$4$$ and its negative are the two zeros of polynomial $$x^4-17x^2+16$$, then other two zeros are

A
$$1$$ and $$2$$

B
$$1 $$ and $$-1$$

C
$$1$$ and $$-2$$

D
$$-1$$ and $$2$$

Solution
Question 7
1 / -0

It is given that two of the zeros of the polynomial $$x^4-4x^3+6x^2-4x+1$$ are same and equal to $$1$$, then can we say that all the zeros are same and equal to $$1$$?

A
Yes

B
No

C
Can't say anything

D
None of these

Solution
Question 8
1 / -0

If two of the zeros of the polynomial $$x^4-9x^3-180x-400$$ are same as that of the polynomials $$x-4$$ and $$x-5$$, then other two zeros are

A
$$20$$and $$-20$$

B
$$2$$ and $$10$$

C
$$\sqrt{20}$$ and $$-\sqrt{20}$$

D
none of these

Solution
Question 9
1 / -0

If $$0$$ and its predecessor are the zeros of the polynomial $$x^4-2x^3-x^2+2x$$, then find the other two zeros.

A
$$2$$ and $$3$$

B
$$2$$ and $$4$$

C
$$-2$$ and $$3$$

D
$$1$$ and $$2$$

Solution
Question 10
1 / -0

If the smallest natural number and its successor are the two zeros of the polynomial $$x^4-3x^3-4x^2+18x-12$$, then other two zeros are ____.

A
$$\sqrt6$$ and $$-\sqrt6$$

B
$$6$$ and $$-\sqrt6$$

C
$$\sqrt6$$ and $$6$$

D
None of the above.

Solution