Polynomials Test

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Polynomials Test - 23

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Question 1
1 / -0

The degree of the polynomial $$2 - y^{2} - y^{3} + 2y^{7}$$ is :

A
2

B
7

C
0

D
3

Solution

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.
Hence, for $$2-y^2-y^3+2y^7$$, the degree$$=7$$
So, answer is $$B$$.
Question 2
1 / -0

Which of the following is a quadratic polynomial in one variable ?

A
$$\sqrt{2x^3}+5$$

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

C
$$x^2$$

D
$$2x^2+y^2$$

Solution

A quadratic polynomial is a polynomial of degree 2.
Here,
$$(A)$$ It is not a polynomial because it has the degree in fraction.
$$(B)$$ It is not a polynomial as:- A polynomial by definition is a function given by one term or a sum of terms with real number coefficients where the power of each variable is a non-negative integer.
$$(C)$$ It is a polynomial of degree $$2$$ and hence correct. $$(Answer)$$
$$(D)$$ It is a polynomial of degree $$2$$ but not in 1 variables.
Question 3
1 / -0

Which of the following is a cubic polynomial ?

A
$$x^{3}+3x^{2}-4x+3$$

B
$$x^{2}+4x-7$$

C
$$3x^{2}+4$$

D
$$3(x^{2}+x+1)$$

Solution

A cubic polynomial is a polynomial of degree $$3$$, or in simpler words highest power of $$x$$ is $$3$$.
It is of the form $$f(x)=a{ x }^{ 3 }+b{ x }^{ 2 }+cx+d$$ where $$a,b,c,d$$ belongs to real numbers.
We can see that in option A, $$x$$ has the highest power $$3$$ and $$a=1,b=3,c=-4$$ and $$d=3$$.
Rest of the options $$B, C, D$$ have the highest power as $$2$$.
Hence, they are quadratic polynomials.

Correct option is $$A$$
Question 4
1 / -0

8 is a polynomial of degree :

A
1

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

C
8

D
0

Solution

Degree of a polynomial is the highest power of the variable in the polynomial.
Degree of $$8$$ is $$0$$ since $$8x^0$$$$=8$$.
Question 5
1 / -0

In figure, the graph of a polynomial p (x) is shown. The number of zeroes of p (x) is :

A
0

B
2

C
1

D
None of these

Solution

Here the no. of zeroes represents the no. of values of x for which p(x) is zero.
So here, we see that the graph cuts the x-axis at 2 points which implies $$p(x)$$ is zero at these 2 points only.
Question 6
1 / -0

The graph of y $$=$$ p(x) is given below.
The number of zeroes of p(x) is :

A
0

B
2

C
4

D
3

Solution

Graph of $$y=p(x)$$ intersects X-axis at three distinct points i.e., two out of which lie in positive X-axis and one on negative X-axis.
So we can say that no of zeros of $$y=p(x)$$ is 3.
Question 7
1 / -0

Which of the following is a cubic polynomial ?

A
$$x^3+3x^2-4x+3$$

B
$$x^2+4x-7$$

C
$$3x^2+4$$

D
$$3(x^2+x+1)$$

Solution

A cubic polynomial is a polynomial with degree 3, where the degree of a polynomial is the highest degree of its monomials (individual terms) with non-zero coefficients.
Hence, in option A the degree is 3 and in rest options, it is 2.
Question 8
1 / -0

A cubic polynomial is a polynomial with degree :

A
1

B
3

C
0

D
2
Question 9
1 / -0

Degree of which of the following polynomials is zero?

A
$$x$$

B
$$15$$

C
$$y$$

D
$$x+x^2$$

Solution

The degree of a polynomial is the highest degree of its monomials (individual terms) with non-zero coefficients.
For, non-zero constants, degree is zero.
Here, $$15$$ is the only non-zero constant and thus has zero degree.
Hence, $$B$$ is correct.
Question 10
1 / -0

If sum of the roots is $$2$$ and product is $$5$$, then the quadratic equation is

A
$$x^2 + 2x + 5 = 0$$

B
$$x^2 - 2x - 5 = 0$$

C
$$x^2 + 2x - 5 = 0$$

D
$$x^2 - 2x + 5 = 0$$

Solution

Given the sum of the roots is 2 and the product of the roots is 5.
Therefore, the quadratic equation is given by $$x^2-$$ (Sum of the roots)$$x +$$ (Product of the roots) $$=0$$.
$$\therefore x^2-2x+5=0$$ is the quadratic equation.

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Re-Attempt Weekly Quiz Competition

Polynomials Test - 23

Result

Polynomials Test - 23

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SHARING IS CARING

Question 1

2

7

0

3

Solution

Question 2

$$\sqrt{2x^3}+5$$

$$2x^2+2x^{-2}$$

$$x^2$$

$$2x^2+y^2$$

Solution

Question 3

$$x^{3}+3x^{2}-4x+3$$

$$x^{2}+4x-7$$

$$3x^{2}+4$$

$$3(x^{2}+x+1)$$

Solution

Question 4

1

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

8

0

Solution

Question 5

0

2

1

None of these

Solution

Question 6

0

2

4

3

Solution

Question 7

$$x^3+3x^2-4x+3$$

$$x^2+4x-7$$

$$3x^2+4$$

$$3(x^2+x+1)$$

Solution

Question 8

1

3

0

2

Question 9

$$x$$

$$15$$

$$y$$

$$x+x^2$$

Solution

Question 10

$$x^2 + 2x + 5 = 0$$

$$x^2 - 2x - 5 = 0$$

$$x^2 + 2x - 5 = 0$$

$$x^2 - 2x + 5 = 0$$

Solution

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