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CBSE Questions for Class 9 Maths Polynomials Quiz 9 - MCQExams.com
CBSE
Class 9 Maths
Polynomials
Quiz 9
If $$2$$ is a root of $$kx^4-11x^3+kx^2+13x+2$$, what is the value of $$k$$?
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$$1$$
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$$2$$
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$$3$$
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$$4$$
Explanation
$$f(2) = k\times (2)^4-11\times (2)^3+k\times (2)^2+13\times 2+2$$
$$f(2)=0$$
$$16k-88+4k+26+2=0$$
$$ 20k -88+28=0$$
$$20k-60=0$$
$$20k =60$$
$$k=3$$
Find the value of $$1.03^2$$ using identity.
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$$1.0409$$
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$$1.0609$$
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$$1.0009$$
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$$1.0309$$
Explanation
Given, $$1.03^2 = (1+0.03)^2$$.
We know, $$(a+b)^2=a^2+2ab+b^2$$.
Then,
$$1.03^2 = (1+0.03)^2$$
$$=1^2+(0.03)^2+2\times 1\times 0.03$$
$$=1+0.0009+0.06$$
$$=1.0609$$.
Therefore, option $$B$$ is correct.
The zero of a polynomial $$P(x)$$ is:
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A number $$c$$ such that $$P(c) = 0$$
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A number $$c$$ such that $$P(-c) = 1$$
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A number $$c$$ such that $$P(c)+P(-c) = 0$$
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none of the above
Explanation
Consider the polynomial, $$p(x) = ax^2 + bx +c$$.
To find the zero of a polynomial, we write $$p(x) = 0$$.
Hence, a real number
$$c$$ is said to be a zero of the polynomial
$$p(x)$$, if
$$p(c)=0$$.
Therefore, option $$A$$ is correct.
Find the value of $$(a-b)(a+b)+(b-c)(b+c)+(c-a)(c+a)$$.
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$$abc$$
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$$a^2+b^2+c^2$$
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$$0$$
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$$1$$
Explanation
We know, $$(a-b)(a+b)=a^2-b^2$$.
$$\therefore (a-b)(a+b)+(b-c)(b+c)+(c-a)(c+a)$$
$$=(a^2-b^2)+(b^2-c^2)+(c^2-a^2)$$
$$=a^2-b^2+b^2-c^2+c^2-a^2$$
$$=0$$.
Therefore, option $$C$$ is correct.
If $$p(x) = 5x - 4$$, then $$p(2) = $$
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$$1$$
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$$6$$
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$$0$$
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$$3$$
Explanation
The polynomial is $$p(x)=5x-4$$ we substitute $$x=2$$ in the polynomial:
$$p(2)=(5\times 2)-4=10-4=6$$
Hence, $$p(2)=6$$.
The _________ power of the variable in a polynomial is called its degree.
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highest
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lowest
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negative
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none of these
Explanation
The polynomial $$x^2+x+a$$ is in the standard form.
The power is simply the number in the exponent.
In the polynomial,
$$x^2+x+a$$
, the power of the first term is $$2$$. Since the polynomial has the largest exponent of the variable $$x$$ as $$2$$, it is the degree of the polynomial.
Hence, the highest power of the variable in a polynomial is called its degree.
If $$p(x) = x^3 - 8x^2 + 4$$, then $$p(4) =$$
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$$68$$
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$$60$$
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$$-60$$
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$$-68$$
Explanation
The polynomial is $$p(x)=x^3-8x^2+4$$ and substitute $$x=4$$ in the polynomial:
$$p(4)=(4)^3-8(4)^2+4=64-(8\times 16)+4=64-128+4=68-128=-60$$
Hence, $$p(4)=-60$$.
If $$p(-2) = 24 $$, then $$p(x) = $$
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$$3x^2 + 5x + 3$$
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$$3x^2 - 5x + 3$$
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$$3x^2 + 5x + 2$$
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$$3x^2 - 5x + 2$$
Explanation
Let $$p(x)=3x^2-5x+2$$ and substitute $$x=-2$$ as shown below:
$$p(-2)=3(-2)^{ 2 }-\left( 5\times -2 \right) +2=\left( 3\times 4 \right) +10+2=12+10+2=24$$
Hence,
$$p(x)=3x^2-5x+2$$.
If $$p(-3) = 27$$, then $$p(x) =$$
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$$4x^2 - 3x$$
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$$4x - 3x$$
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$$4x^2 + 3x$$
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$$4x^2 + 3$$
Explanation
Consider option A
let $$p(x)=4x^2-3x$$. Then $$p(-3)=4(9)+9=45$$ Hence $$p(-3)\neq 27$$.
Consider option B
let $$p(x)=4x-3x=x$$. Then $$p(-3)=-3$$ Hence $$p(-3)\neq 27$$.
Consider option C
let $$p(x)=4x^2+3x$$. Then $$p(-3)=4(9)-9=27$$ Hence $$p(-3)=27$$.
Consider option D
let $$p(x)=4x^2+3$$. Then $$p(-3)=4(9)+3=39$$ Hence $$p(-3)\neq 27$$.
Hence the correct option is option C.
If $$p(x) = 5x^2 - 4x + 2$$, then $$p(3) =$$
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$$35$$
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$$30$$
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$$45$$
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$$33$$
Explanation
The given polynomial is $$p(x)=5x^2-4x+2$$ we substitute $$x=3$$ in the polynomial:
$$p(3)=5(3)^2-4(3)+2=5\times 9-12+2=45-12+2=47-12=35$$
Hence, $$p(3)=35$$.
If $$p(1) = 8$$, then $$ p(x) = $$
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$$3x + 6$$
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$$3x + 3$$
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$$3x + 4$$
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$$3x + 5$$
Explanation
Let $$p(x)=3x+5$$ and substitute $$x=1$$ as shown below:
$$p(1)=\left( 3\times 1 \right) +5\\=3+5\\=8$$
Hence,
$$p(x)=3x+5$$
.
The highest power of the variable in a polynomial is called its _______.
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degree
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constant
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zero
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co-efficient
Explanation
The polynomial $$x^2+x+a$$ is in the standard form.
The power is simply number in the exponent. In the polynomial, $$x^2+x+a$$, the power of the first term is $$2$$. Since the polynomial has the largest exponent that is $$2$$, which is the degree of the polynomial.
Hence, the highest power of the variable in a polynomial is called its degree.
$$5x + 3$$ is a polynomial in $$x$$ of degree
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$$2$$
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$$1$$
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$$3$$
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$$5$$
Explanation
The given polynomial is $$5x+3$$
The power of $$x$$ in the first term is $$1$$,and the power of $$x$$ in the second term is $$0$$
Since in the polynomial the largest exponent of $$x$$ is $$1$$, it is the degree of the polynomial.
Hence, the degree of the polynomial is $$1$$
$$p(a) = 3a^2 + 4a - 4$$ is a polynomial in $$a$$ of degree
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$$4$$
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$$3$$
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$$2$$
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$$1$$
Explanation
The polynomial $$ax^2+bx+c$$ is in standard form.On comparing
$$3a^2+4a-4$$ with the standard polynomial we see
, the power of the first term is $$2$$. Since the polynomial has the largest exponent, that is $$2$$ which is the degree of the polynomial.
Hence, the degree of the polynomial is $$2$$.
Which of the following is NOT a constant polynomial?
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$$p(x) = 15$$
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$$p(x) = 1$$
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$$p(x) = x$$
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$$p(x) = 20$$
Explanation
$$\textbf{Step-1: Apply the concept of polynomial.}$$
$$\text{Since}$$
$$p(x)=x$$
$$\text{is a polynomial with variable}$$
$$x$$
$$\text{and there is no constant term in it.}$$
$$\text{In the other given options, we can see that the polynomials have}$$
$$\text{constant terms, none of them has any variable term.}$$
$$\text{So,}$$
$$p(x)=x$$
$$\text{is not a constant polynomial.}$$
$$\textbf{Hence, correct option is C}$$
Which of the following polynomial defines constant polynomials?
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$$p(x) = ax^3 + bx^2 + cx + d$$
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$$p(x) = ax^2 + bx + c$$
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$$p(x) = c$$
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$$p(x) = ax + b$$
Explanation
Since a polynomial $$p(x)=c$$ is a constant polynomial with constant term $$c$$,
A polynomial $$ax^2+bx+c$$ is a quadratic polynomial with variables $$x,y$$ and constant $$c$$ and
A polynomial $$ax+b$$ is a linear polynomial with variable $$x$$ and constant $$b$$
Hence, $$p(x)=c$$ is a constant polynomial.
$$p(y) = 5y^3 - 2y^2 + y + 10$$ is a polynomial in $$y$$ of degree
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$$0$$
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$$1$$
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$$2$$
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$$3$$
Explanation
in
$$5y^3-2y^2+y+10$$ we see
the power of the first term is $$3$$,
the power of the second term is $$2$$ and
the power of the third term is $$1$$
.
Since the polynomial has the largest exponent, that is $$3$$ which is the degree of the polynomial.
Hence, the degree of the polynomial is $$3$$.
Which of the following is a constant polynomial?
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$$p(x) = \dfrac{15}{2}$$
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$$p(x) = x$$
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$$p(x) = x^2$$
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$$p(x) = x^3$$
Explanation
$$\textbf{Step-1: Apply the concept of polynomial.}$$
$$\text{We know that, a constant polynomial is a polynomial}$$
$$\text{that has only constant term and no variables.}$$
$$\text{Since,}$$
$$p(x)=\dfrac { 15 }{ 2 },$$
$$\text{is a polynomial with constant term}$$
$$\dfrac { 15 }{ 2 }$$
$$ \text{having no variable, it is a constant polynomial.}$$
$$\text{So,}$$
$$p(x)=\dfrac { 15 }{ 2 },$$
$$\text{is a constant polynomial.}$$
$$\textbf{Hence, correct option is A}$$
Which of the following is a constant polynomial?
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$$p(x) = 7 + 3x$$
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$$p(x) = 7 $$
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$$p(x) = 7x + 7$$
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$$p(x) = 4x + 3$$
Explanation
Since $$p(x)=7$$ is a polynomial with constant term $$7$$ and there is no variable in it.
Hence, $$p(x)=7$$ is a constant polynomial.
$$p(x) = c$$, where $$c$$ is a real number. $$p(x)$$ is a
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linear polynomial
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quadratic polynomial
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cubic polynomial
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constant polynomial
Explanation
Since $$p(x)=c$$ is a polynomial with only constant term
$$c$$
and no variable term present in the it.
Hence, $$p(x)$$ is a constant polynomial.
$$p(x) = 6x^2 - 2x^6 $$ is a polynomial in $$x$$ of degree
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$$6$$
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$$3$$
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$$1$$
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none of these
Explanation
$$p(x) = 6x^2 - 2x^6$$.
Here, the highest degree of the variable $$x$$ is $$6$$.
$$\therefore p(x)$$ is a polynomial of degree $$6$$
$$p(5) = 5$$ then, which polynomial from the following, it corresponds to?
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$$p(x) = x^2 - 5x + 5$$
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$$p(x) = x^2 - 5x$$
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$$p(x) = x^2 - x + 5$$
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$$p(x) = x^2 $$
Explanation
Let $$p(x)=x^2-5x+5$$ and substitute $$x=5$$ as shown below:
$$p(5)=(5)^{ 2 }-\left( 5\times 5 \right) +5=25-25+5=5$$
Hence,
$$p(x)=x^2-5x+5$$
.
What is the degree of the polynomial $$p(x) = 5x^3 - 8x^2 + 4x?$$
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$$3$$
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$$2$$
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$$1$$
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$$0$$
Explanation
The polynomial $$ax^3+ bx^2+cx+d=0$$
is in standard form.
On comparing
$$5x^3-8x^2+4x$$ with the standard form,
the power of the first term is $$3$$,
the power of the second term is $$2$$ and
the power of the third term is $$1$$
. Since the polynomial has the largest exponent, that is $$3$$ which is the degree of the polynomial.
Hence, the degree of the polynomial is $$3$$
What is the degree of the polynomial $$p(x) = 8x^8 + 9x^9 + 10x^0$$?
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$$8$$
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$$9$$
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$$10$$
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$$0$$
Explanation
After writing the
$$9x^9+8x^8+10x^0$$ we can see that
the power of the first term is $$9$$,
the power of the second term is $$8$$ and
the power of the third term is $$0$$
. Since the polynomial has the largest exponent, that is $$9$$ which is the degree of the polynomial.
Hence, the degree of the polynomial is $$9$$.
The constant polynomial whose coefficients are all equal to $$0$$ is called ________ polynomial.
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Zero
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Linear
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Quadratic
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Cubic
Explanation
For example:-
Consider the polynomial, $$p(x) = ax^2 + bx +c$$ , if $$a=b=c= 0$$ then the expression becomes zero polynomial.
Therefore, zero polynomial can be written as $$p(x) = 0$$.
Hence, the constant polynomial whose coefficients are all equal to $$0$$ is called a zero polynomial.
A polynomial whose coefficients are all equal to _______ is called zero polynomial.
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$$1$$
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$$2$$
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$$3$$
0%
$$0$$
Explanation
Consider the polynomial, $$p(x) = ax^2 + bx +c$$ , if $$a=b=c= 0$$ then the expression becomes zero polynomial.
Therefore, zero polynomial can be written as $$p(x) = 0$$.
Hence, the constant polynomial whose coefficients are all equal to $$0$$ is called a zero polynomial.
Which of the following is not a constant polynomial?
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$$p(x) = 3^3$$
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$$p(x) = 2^3$$
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$$p(x) = x^3$$
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$$p(x) = 4^3$$
Explanation
$$\textbf{Step-1: Apply the concept of polynomial.}$$
$$\text{We know that cubic power of a constant is also a constant.}$$
$$\text{Therefore,}$$
$$p(x)=x^3$$ $$\text{is a polynomial with variable}$$
$$x$$
$$\text{and there is no constant term in it.}$$
$$\text{So,}$$
$$p(x)=x^3$$
$$\text{is not a constant polynomial.}$$
$$\textbf{Hence, correct option is C}$$
Which of the following polynomials, has $$p(6) = 36$$ value?
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$$p(x) = x$$
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$$p(x) = x^2$$
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$$p(x) = x^3$$
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$$p(x) = x^0$$
Explanation
Let $$p(x)=x^2$$ and substitute $$x=6$$ as shown below:
$$p(6)=(6)^{ 2 }=36$$
Hence,
$$p(x)=x^2$$
.
For $$p(x) = 3x^2 - 5x, p(6) = $$
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$$36$$
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$$72$$
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$$78$$
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$$77$$
Explanation
The polynomial given to us is
$$p(x)=3x^2-5x$$
after substituting the value of $$x=6$$ in the polynomial:
$$p(6)=3(6)^2-(5\times 6)=(3\times 36)-30=108-30=78$$
Hence, $$p(6)=78$$.
Zero polynomial can be written as ________.
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$$p(x) = x$$
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$$p(x) = 1$$
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$$p(x) = 0$$
0%
$$p(x) = x^2$$
Explanation
Consider the polynomial, $$p(x) = ax^2 + bx +c$$ , if $$a=b=c= 0$$ then the expression becomes zero polynomial.
Therefore
, the constant polynomial whose coefficients are all equal to $$0$$ is called a zero polynomial.
Hence, zero polynomial can be written as $$p(x) = 0$$.
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