Polynomials Test

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Polynomials Test - 25

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Question 1
1 / -0

$$(a + b)^{2} = (a + b)\times$$ ____

A
$$ab$$

B
$$2ab$$

C
$$(a + b)$$

D
$$(a - b)$$

Solution

We know that $$x^{2}=x\times x$$
Then $$(a+b)^{2}=(a+b)\times (a+b)$$

Hence, the answer is (C)
Question 2
1 / -0

The root of the polynomial equation $$3x-1=0$$ is

A
$$x=-\dfrac{1}{3}$$

B
$$x=\dfrac{1}{3}$$

C
$$x=1$$

D
$$x=3$$

Solution

Given: $$3x-1=0$$

$$\Rightarrow 3x=1$$

$$\Rightarrow x=\dfrac{1}{3}$$

Hence root of $$3x-1=0$$ is $$\dfrac{1}{3}$$
Question 3
1 / -0

The degree of the polynomial $$4x^2-7x^3+6x+1$$ is.

A
2

B
1

C
3

D
0

Solution

A polynomial is a function of the form $$f(x) = a_{n}x^{n} + a_{n−1}x^{n−1} + ... + a_{2}x^{2} + a_1x + a_0 $$
where $$a_{n}, a_{n−1} , ... a_{2} ,a_1 , a_0 $$ . are contants and $$n$$ is a natural number.

Let $$p(x) = 4x^{2}-7x^{3}+6x+1$$
$$\Rightarrow$$The degree of a polynomial is the highest power of $$x$$ in its expression.

$$\Rightarrow$$Highest power of $$x$$ in $$p(x) $$ is $$=3

Thus, the degree $$=3$$

$$p(x) = 4x^{2}-7x^{3}+6x+1 $$ is a cubic polynomial.
Hence, option $$C $$ is correct.
Question 4
1 / -0

The roots of the polynomial equation $$x^2+2x=0$$ are:

A
$$x=0, 2$$

B
$$x=1, 2$$

C
$$x= 1, -2$$

D
$$x=0, -2$$

Solution

The given equation is $$ x^2+2x=0$$

$$x\times(x+2)=0$$

$$x=0$$ or $$x+2=0$$

$$\therefore x=0 $$ or $$ x=-2$$
Question 5
1 / -0

The degree of $$(6{x}^{7} -7{x}^{3} + 3{x}^{2} + 2x -1)$$ is ______.

A
$$7$$

B
$$6$$

C
$$3$$

D
$$5$$

Solution

The degree is the highest power of an exponent in the polynomial.
In the given polynomial,
$$(6{x}^{7} -7{x}^{3} + 3{x}^{2} + 2x -1)$$

It can be clearly observed that the first term $$6{x}^{7}$$ has the highest power of $$x$$ i.e $$7$$.

Thus, the degree of the given polynomial is $$7$$.

Hence, $$7$$ is the correct answer.
Question 6
1 / -0

The zero of the polynomial $$P(x)=\sqrt { 5 } x-5$$

A
$$\sqrt { 5 } $$

B
$$-\sqrt { 5 } $$

C
$$\cfrac { \sqrt { 5 } }{ 5 } $$

D
$$-5$$

Solution

Given polynomial is $$P(x)=\sqrt { 5 } x-5$$.

To get the zeros of $$P(x)$$, equate it to zero,
$$\Rightarrow\sqrt { 5 } x-5=0$$
$$\Rightarrow\sqrt{5} x=5$$
$$\Rightarrow x=\sqrt { 5 } $$

Hence, the zero of $$P(x)$$ is $$\sqrt{5}$$.
Question 7
1 / -0

Number of zeros of the 'zero polynomial' is equal to?

A
$$0$$

B
$$1$$

C
$$2$$

D
Infinite

Solution

A zero polynomial is a polynomial of the form $$P(x)=0$$ where all coefficients of the polynomial are equal to zero.

Any value of $$x$$ can be a zero of a zero polynomial.

So, number of zeroes of a zero polynomial $$=$$ $$infinite$$. $$[D]$$
Question 8
1 / -0

The degree of $$(6x^{4} - 7x^{3} + 3x^{2} + 2x - 1)$$ is _______.

A
$$4$$

B
$$6$$

C
$$3$$

D
$$5$$

Solution

Given polynomial is $$6x^4-7x^3+3x^2+2x-1$$
For the given polynomial, highest power of $$x$$ is $$4$$.
And it should be Integer,
Thus degree of polynomial is $$4$$.
Question 9
1 / -0

The degree of the polynomial $$p(x) =x^7 - 5x^3 - 3x^2 + 2x$$ is _____

A
$$7$$

B
$$2$$

C
$$3$$

D
$$1$$

Solution

Given the polynomial is $$p(x) =x^7 - 5x^3 - 3x^2 + 2x$$.
Now the power of the highest degree term is $$7$$ so the degree of the polynomial is $$7$$.
Question 10
1 / -0

Zeros of the polynomial p (x) = $$x^{2}-2x$$ is /are

A
$$0,2$$

B
$$0,1$$

C
$$1,2$$

D
$$2,3$$

Solution

Zeros of the polynomial $$x^2-2x=p(x)$$

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

$$\Rightarrow x(x-2)=0$$

$$\Rightarrow x=0$$ or $$x=2$$

$$\therefore$$ Zeros of polynomial $$p(x)$$ are $$0$$ and $$2$$.

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Polynomials Test - 25

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Polynomials Test - 25

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Question 1

$$ab$$

$$2ab$$

$$(a + b)$$

$$(a - b)$$

Solution

Question 2

$$x=-\dfrac{1}{3}$$

$$x=\dfrac{1}{3}$$

$$x=1$$

$$x=3$$

Solution

Question 3

2

1

3

0

Solution

Question 4

$$x=0, 2$$

$$x=1, 2$$

$$x= 1, -2$$

$$x=0, -2$$

Solution

Question 5

$$7$$

$$6$$

$$3$$

$$5$$

Solution

Question 6

$$\sqrt { 5 } $$

$$-\sqrt { 5 } $$

$$\cfrac { \sqrt { 5 } }{ 5 } $$

$$-5$$

Solution

Question 7

$$0$$

$$1$$

$$2$$

Infinite

Solution

Question 8

$$4$$

$$6$$

$$3$$

$$5$$

Solution

Question 9

$$7$$

$$2$$

$$3$$

$$1$$

Solution

Question 10

$$0,2$$

$$0,1$$

$$1,2$$

$$2,3$$

Solution

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