Polynomials Test

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Polynomials Test - 24

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Weekly Quiz Competition

Question 1
1 / -0

Find the polynomial with degree $$6$$.

A
$$6{ x }^{ 4 }+7{ x }^{ 2 }$$

B
$$8{ x }^{ 4 }{ y }^{ 2 }+7{ x }^{ 5 }{ y }^{ 3 }-\dfrac { 3 }{ 5 } $$

C
$$8{ x }^{ 2 }{ y }^{ 2 }{ z }^{ 2 }+7{ x }^{ 2 }{ y }^{ 2 }z+3{ x }^{ 4 }$$

D
$$8{ x }^{ 6 }{ y }^{ 6 }+{ y }^{ 2 }+7{ x }^{ 3 }$$

Solution

In the case of a polynomial in one variable, the highest power of the variable is called the degree of the polynomial.

In the case of polynomials in more than one variable, the sum of the powers of the variables in each term is taken up and the highest sum so obtained is called the degree of the polynomial.

$$(A)6x^{4}+7x^{2}$$
The highest power of this expression is 4.Then degree is 4.

$$(B)8x^{4}y^{2}+7x^{5}y^{3}-\frac{3}{5}$$
The highest power of this expression is 5+3=8. Then degree is 8.

$$(C)8x^{2}y^{2}z^{2}+7x^{2}y^{2}z+3x^{4}$$
The highest power of this expression is 2+2+2=6. Then degree is 6.

$$(D)8x^{6}y^{6}+y^{2}+7x^{3}$$
The highest power of this expression is 6+6=12. Then degree is 12.

In all option (C) is the expression with degree 6
Question 2
1 / -0

The zero(s) of $$p(x) = 5x - 4$$ is/are:

A
$$-4$$

B
$$5$$

C
$$\dfrac{4}{5}$$

D
$$- \dfrac{4}{5}$$

Solution

$$p(x) = 5x - 4$$
A linear polynomial has at most one zero and to find that we equate the polynomial to zero
$$\implies 5x - 4 = 0$$
$$\implies 5x = 4$$
$$\therefore x = \dfrac {4}{5}$$.

Therefore, option $$C$$ is correct.
Question 3
1 / -0

Find the solution of $$(2x+6)^2$$.

A
$$x^2+24x+36$$

B
$$4x^2+24x+6$$

C
$$4x^2+24x+36$$

D
$$4x^2-24x+36$$

Solution

$$(2x+6)^2 = (2x+6)(2x+6)$$
= $$2x.2x+2x.6+6.2x+6.6$$
= $$4x^2+12x+12x+36$$
= $$4x^2+24x+36$$
Question 4
1 / -0

Find a zero of the polynomial $$p(x) = 3x + 1$$

A
$$\dfrac {1}{3}$$

B
$$\dfrac {-1}{3}$$

C
$$3$$

D
$$-3$$

Solution

Finding a zero of $$p(x)$$, is same as solving the equation
$$p(x) = 0$$
i.e. $$3x + 1 = 0$$
$$\Rightarrow 3x = -1$$
$$\Rightarrow x = -\dfrac {1}{3}$$
So, $$-\dfrac {1}{3}$$ is a zero of the polynomial $$3x + 1$$.
Question 5
1 / -0

Find the zero of the polynomial $$f(x) = x - 2$$ :

A
$$-2$$

B
$$2$$

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

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

Solution

Given polynomial is $$f(x)=x-2$$
We know that a polynomial is zero polynomial when $$f(x)=0$$
Then $$x-2=0$$
Add $$2$$ on both sides, we get
$$x-2+2=2$$
$$\Rightarrow x=2$$
So, value of $$x$$ is $$2$$ for zero polynomial.
Question 6
1 / -0

Find zero of the polynomial $$f(x) = x + 2$$ :

A
$$0$$

B
$$-2$$

C
$$2$$

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

Solution

Given polynomial is $$f(x)=x+2$$
We know that a polynomial is zero polynomial when $$f(x)=0$$.
Then $$x+2=0$$
On subtracting $$2$$ on both the sides, we get
$$x+2-2=-2$$
$$\Rightarrow x=-2$$
So, value of $$x$$ is $$-2$$ for zero polynomial.
Question 7
1 / -0

Find the zero of the polynomial $$f(x) = 2x + 3$$.

A
$$-\dfrac {3}{2}$$

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

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

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

Solution

Given polynomial $$f(x)=2x+3$$
We know that by putting $$f(x)=0$$ and solving for $$x$$ we can find the zeroes of a polynomial.
$$\therefore 2x+3=0$$
Add -3 both side we get
$$2x+3-3=-3$$
$$\Rightarrow 2x=-3$$
Divided by 2 both sides we get
$$x=-\dfrac{3}{2}$$
So value of zero of the polynomial is $$-\dfrac{3}{2}$$
Question 8
1 / -0

The degree of the polynomial $$2x^{2} - 4x^{3} + 3x + 5$$ is

A
$$0$$

B
$$1$$

C
$$2$$

D
$$3$$

Solution

The degree of the polynomial means the highest power of the variable.
Therefore, the degree of the polynomial $$2x^2-4x^3+3x+5$$ is $$3$$.
Question 9
1 / -0

The degree of the polynomial $$5x^7 - 6x^5 + 7x - 6$$ is

A
$$4$$

B
$$5$$

C
$$6$$

D
$$7$$

Solution

The degree of a polynomial is the highest exponent of variable.
Here highest exponent is $$7$$.
So, the degree is $$7$$.
Option $$D$$ is correct.
Question 10
1 / -0

The degree of the polynomial $$x^{2} - 5x^{4} +\dfrac {3}{4}x^{7} - 73x + 5$$ is ____

A
$$7$$

B
$$\dfrac {3}{4}$$

C
$$4$$

D
$$-73$$

Solution

Given equation is $$P(x)=x^{2}-5x^{4}+\dfrac{3}{4}x^{7}-73x+5$$
We know that, the degree of a polynomial is the highest power of its variables when the polynomial is expressed in its canonical form consisting of a linear combination of monomials.
In the given equation, $$7$$ is the highest power
Then, the degree of polynomial $$P(x)$$ is $$7$$.

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Polynomials Test - 24

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Polynomials Test - 24

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Question 1

$$6{ x }^{ 4 }+7{ x }^{ 2 }$$

$$8{ x }^{ 4 }{ y }^{ 2 }+7{ x }^{ 5 }{ y }^{ 3 }-\dfrac { 3 }{ 5 } $$

$$8{ x }^{ 2 }{ y }^{ 2 }{ z }^{ 2 }+7{ x }^{ 2 }{ y }^{ 2 }z+3{ x }^{ 4 }$$

$$8{ x }^{ 6 }{ y }^{ 6 }+{ y }^{ 2 }+7{ x }^{ 3 }$$

Solution

Question 2

$$-4$$

$$5$$

$$\dfrac{4}{5}$$

$$- \dfrac{4}{5}$$

Solution

Question 3

$$x^2+24x+36$$

$$4x^2+24x+6$$

$$4x^2+24x+36$$

$$4x^2-24x+36$$

Solution

Question 4

$$\dfrac {1}{3}$$

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

$$3$$

$$-3$$

Solution

Question 5

$$-2$$

$$2$$

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

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

Solution

Question 6

$$0$$

$$-2$$

$$2$$

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

Solution

Question 7

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

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

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

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

Solution

Question 8

$$0$$

$$1$$

$$2$$

$$3$$

Solution

Question 9

$$4$$

$$5$$

$$6$$

$$7$$

Solution

Question 10

$$7$$

$$\dfrac {3}{4}$$

$$4$$

$$-73$$

Solution

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