Polynomials Test

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Polynomials Test - 22

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Weekly Quiz Competition

Question 1
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 2
1 / -0

Which type of polynomial is $$y^3-y$$ ?

A
Linear Polynomial

B
Quadratic Polynomial

C
Cubic Polynomial

D
None of above

Solution

$$ { y }^{ 3 } - y$$ is a cubic polynomial as the highest power of $$x$$ is $$3.$$
Question 3
1 / -0

Which type of Polynomial is $$t^{2}$$ ?

A
Linear Polynomial

B
Quadratic Polynomial

C
Cubic Polynomial

D
None of above

Solution

The degree of the given expression is 2. So, it is a quadratic polynomial.
Question 4
1 / -0

Which type of polynomial is $$1 + x + x^2$$ ?

A
Linear Polynomial

B
Quadratic Polynomial

C
Cubic Polynomial

D
None of above

Solution

The degree of the equation is $$2$$. So, it is a quadratic polynomial.
Question 5
1 / -0

If $$\alpha$$ and $$\beta$$ are the zeroes of the polynomial $$4x^{2} + 3x + 7$$, then $$\dfrac{1}{\alpha }+\dfrac{1}{\beta }$$ is equal to:

A
$$\dfrac{7}{3}$$

B
$$-\dfrac{7}{3}$$

C
$$\dfrac{3}{7}$$

D
$$-\dfrac{3}{7}$$

Solution

Given: $$\alpha, \beta$$ are zeroes of the polynomial $$4x^2+3x+7$$
To find the value of $$\dfrac 1\alpha+\dfrac 1\beta$$
We know that equation $$ax^{2}+bx+c=0$$
Then sum of roots $$=\dfrac{-b}{a}$$ and product of roots$$=\dfrac{c}{a}$$
From the given quadratic equation,
$$\alpha+\beta=-\dfrac 34$$ and $$\alpha\beta=\dfrac 74$$
Therefore,
$$\dfrac 1\alpha+\dfrac 1\beta=\dfrac {\alpha+\beta}{\alpha\beta}$$

$$=\dfrac {-\dfrac 34}{\dfrac 74}=-\dfrac{3}{7}$$

$$\Rightarrow \dfrac 1\alpha+\dfrac 1\beta = -\dfrac 37$$
Question 6
1 / -0

Which type of polynomial is $$(2+x)$$ ?

A
Linear Polynomial

B
Quadratic Polynomial

C
Cubic Polynomial

D
None of above

Solution

The degree of the equation is $$1$$. A polynomial with degree $$1$$ is called a linear polynomial. So it is a Linear Polynomial.
Question 7
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 8
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 9
1 / -0

Classify the following as a constant, linear, quadratic, and cubic polynomial:
$$\sqrt{2}x-1$$

A
Linear

B
Quadratic

C
Cubic

D
None of these

Solution

Here, the degree of $$x$$ is $$1$$. Therefore it is a Linear Polynomial.
Question 10
1 / -0

Which of the following is quadratic polynomial

A
$$x + 2$$

B
$$x^{2}+2$$

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

D
$$2x+2$$

Solution

A quadratic polynomial, is a polynomial of degree 2.
Hence $$x^2+2$$ is the only quadratic polynomial out of the four given polynomials.

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Re-Attempt Weekly Quiz Competition

Polynomials Test - 22

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Polynomials Test - 22

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Question 1

$$2$$

$$0$$

$$1$$

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

Solution

Question 2

Linear Polynomial

Quadratic Polynomial

Cubic Polynomial

None of above

Solution

Question 3

Linear Polynomial

Quadratic Polynomial

Cubic Polynomial

None of above

Solution

Question 4

Linear Polynomial

Quadratic Polynomial

Cubic Polynomial

None of above

Solution

Question 5

$$\dfrac{7}{3}$$

$$-\dfrac{7}{3}$$

$$\dfrac{3}{7}$$

$$-\dfrac{3}{7}$$

Solution

Question 6

Linear Polynomial

Quadratic Polynomial

Cubic Polynomial

None of above

Solution

Question 7

Linear Polynomial

Constant Polynomial

Cubic Polynomial

Quadratic Polynomial

Solution

Question 8

$$x^{20}+1$$

$$x^{19}+1$$

$$20x+1$$

$$20xy+1$$

Solution

Question 9

Linear

Quadratic

Cubic

None of these

Solution

Question 10

$$x + 2$$

$$x^{2}+2$$

$$x^{3}+2$$

$$2x+2$$

Solution

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