Polynomials Test

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Polynomials Test - 43

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Weekly Quiz Competition

Question 1
1 / -0

Find the zeroes of the polynomial $$4-\dfrac{1}{2}x^2$$

A
2

B
$$2\sqrt{2}$$

C
0

D
4

Solution

$$4-\dfrac{1}{2}x^2=0$$
$$\dfrac{1}{2}x^2=4$$
$$x^2=8$$
$$\therefore x=\pm 2\sqrt{2}$$
$$\therefore$$ The zeroes of the given polynomial $$2\sqrt{2}$$.
Question 2
1 / -0

Which of the following are the zeroes of the quadratic polynomial $$9-4x^2$$?

A
4

B
9

C
$$\dfrac{3}{2}$$

D
$$\dfrac{2}{3}$$

Solution

$$9-4x^2=0$$
$$4x^2=9$$
$$x^2=\dfrac{9}{4}$$
$$\therefore x=\pm \dfrac{3}{2}$$
$$\therefore$$ The zeroes of the given polynomial are $$\dfrac{3}{2}$$and $$-\dfrac{3}{2}$$.
Question 3
1 / -0

The zeroes of the polynomials, $$t^2 15$$ are.

A
$$\pm \sqrt{15}$$

B
$$\pm \sqrt{5}$$

C
$$\pm \sqrt{3}$$

D
$$\pm 3$$

Solution

$$t^2 – 15=0$$
$$t^2=15$$
$$t=\pm \sqrt{15}$$
Question 4
1 / -0

The degree of a quadratic polynomial is:

A
$$0$$

B
$$1$$

C
$$2$$

D
$$3$$

Solution

The highest power of the variable in a polynomial in one variable is called the degree of the polynomial.

Quadratic polynomial is a polynomial in which highest order of the variable is $$2$$.

For example, $$2x^2+5x+1=0$$ is a quadratic equation and it has a degree $$2$$.

Thus, degree of quadratic polynomial is $$2$$.

Therefore, option $$C$$ is correct.
Question 5
1 / -0

If $$f(x) = 8$$then$$ f(x)$$ is called

A
Constant polynomials

B
linear polynomials

C
quadratic polynomials

D
Cubic polynomials

Solution

If $$f(x) = 8$$ then $$ f(x)$$ is called Constant polynomials
Question 6
1 / -0

The degree of polynomial is $$x + 2$$ is:

A
$$2$$

B
$$1$$

C
$$3$$

D
$$4$$

Solution

$$\textbf{Step 1: Apply the property of polynomial.}$$

$$\text{We have, x + 2}$$
  $$\text{We know that the highest power of the variable in a polynomial in one variable is }$$
  $$\text{called the degree of the polynomial.}$$
  $$\text{Here, the highest power of variable x is 1.}$$

$$\textbf{Thus, degree of polynomial is 1, option - (B).}$$
Question 7
1 / -0

Write the correct alternative answer for the following question:
Which is the degree of the polynomial $$ 2x^{2} + 5x^{3} + 7 $$ ?

A
$$3$$

B
$$2$$

C
$$5$$

D
$$7 $$

Solution

The given polynomial is $$ 2x^{2} + 5x^{3} + 7 $$.

We know, in a polynomial in one variable, the highest power of the polynomial term with a non-zero coefficient, is called the degree of the polynomial.
Here, the highest power of the variable $$x$$ is $$3$$.

$$\therefore$$ The degree of the given polynomial is $$3$$.
Therefore, option $$A$$ is correct.
Question 8
1 / -0

The degree of the polynomial $$x^4 + x^3$$ is:

A
$$2$$

B
$$3$$

C
$$5$$

D
$$4$$

Solution

The highest power of the variable in a polynomial in one variable is called the degree of the polynomial.

Here, in the given polynomial $$x^4 + x^3$$, the highest power of the variable $$x$$ is $$4$$.
$$\therefore$$ The degree of the given polynomial is $$4$$.

Therefore, option $$D$$ is correct.
Question 9
1 / -0

The number of zeroes of linear polynomial at most is

A
$$0$$

B
$$1$$

C
$$2$$

D
$$3$$

Solution

$$\textbf{Step-1: Explanation for number of zeroes of linear polynomial}$$
$$\text{The number of zeroes of a polynomial is equal to the degree of the polynomial}$$
$$\text{As the degree of a linear polynomial is 1, the number of zeroes is 1}$$

$$\textbf{Therefore, the number of zeroes of the linear polynomial at most is 1}$$
Question 10
1 / -0

One zero of $$p(x)=2x+1$$ will be

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

B
$$3$$

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

D
$$1$$

Solution

$$p(x)=2x+1$$
For zeroes $$p(x)=0$$
$$0=2x+1$$
$$\Rightarrow x=\dfrac {-1}{2}$$

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Re-Attempt Weekly Quiz Competition

Polynomials Test - 43

Result

Polynomials Test - 43

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SHARING IS CARING

Question 1

2

$$2\sqrt{2}$$

0

4

Solution

Question 2

4

9

$$\dfrac{3}{2}$$

$$\dfrac{2}{3}$$

Solution

Question 3

$$\pm \sqrt{15}$$

$$\pm \sqrt{5}$$

$$\pm \sqrt{3}$$

$$\pm 3$$

Solution

Question 4

$$0$$

$$1$$

$$2$$

$$3$$

Solution

Question 5

Constant polynomials

linear polynomials

quadratic polynomials

Cubic polynomials

Solution

Question 6

$$2$$

$$1$$

$$3$$

$$4$$

Solution

Question 7

$$3$$

$$2$$

$$5$$

$$7 $$

Solution

Question 8

$$2$$

$$3$$

$$5$$

$$4$$

Solution

Question 9

$$0$$

$$1$$

$$2$$

$$3$$

Solution

Question 10

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

$$3$$

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

$$1$$

Solution

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