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CBSE Questions for Class 9 Maths Polynomials Quiz 12 - MCQExams.com
CBSE
Class 9 Maths
Polynomials
Quiz 12
If
f
(
x
)
=
8
then
f
(
x
)
is called
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0%
Constant polynomials
0%
linear polynomials
0%
quadratic polynomials
0%
Cubic polynomials
Explanation
If
f
(
x
)
=
8
then
f
(
x
)
is called Constant polynomials
The degree of polynomial is
x
+
2
is:
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0%
2
0%
1
0%
3
0%
4
Explanation
Step 1: Apply the property of polynomial.
We have, x + 2
We know that the highest power of the variable in a polynomial in one variable is
called the degree of the polynomial.
Here, the highest power of variable x is 1.
Thus, degree of polynomial is 1, option - (B).
Write the correct alternative answer for the following question:
Which is the degree of the polynomial
2
x
2
+
5
x
3
+
7
?
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3
0%
2
0%
5
0%
7
Explanation
The given polynomial is
2
x
2
+
5
x
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
.
∴
The degree of the given polynomial is
3
.
Therefore, option
A
is correct.
The degree of the polynomial
x^4 + x^3
is:
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2
0%
3
0%
5
0%
4
Explanation
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.
The number of zeroes of linear polynomial at most is
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0
0%
1
0%
2
0%
3
Explanation
\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}
Zero of the polynomial
p(x) = \sqrt{3}x + 3
is
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-\sqrt{3}
0%
\dfrac{-\sqrt 3}{3}
0%
\dfrac{3}{\sqrt 3}
0%
3\sqrt 3
One zero of
p(x)=2x+1
will be
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\dfrac {1}{2}
0%
3
0%
\dfrac {-1}{2}
0%
1
Explanation
p(x)=2x+1
For zeroes
p(x)=0
0=2x+1
\Rightarrow x=\dfrac {-1}{2}
State True/False:-
One of the zeroes of the polynomial
x^{2} + 2x - 15
is
11
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True
0%
False
Explanation
To find the zeroes of the polynomial, we have to proceed in the following way:-
Let f(x)=
x^2+2x-15
For zeroes
f(x)=0
\Rightarrow x^2+2x-15=0
\Rightarrow x^2+5x-3x-15=0
\Rightarrow x(x+5)-3(x+5)=0
\Rightarrow (x-3)(x+5)=0
x-3=0
or
x+5=0
x=3
or
x=-5
Hence the zeroes of the polynomial
x^2+2x-15
are
3,-5
.
Hence, given statement is
false.
Identify the zeroes of the given polynomial.
p(z)=4z^2-15z\pi -4\pi ^3
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4\pi ,\frac{-\pi }{4}
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-4\pi ,\frac{\pi }{4}
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4\pi ,\frac{\pi }{4}
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-4\pi ,\frac{-\pi }{4}
For
p(x) = 5x^2 - \dfrac{2}{3} x + 8
, then value of
p (3) =
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50
0%
51
0%
55
0%
35
Explanation
The polynomial given is
p(x)=5x^{ 2 }-\frac { 2 }{ 3 } x+8
after substituting the value
x=3
in the polynomial we get:
p(3)=5x^{ 2 }-\frac { 2 }{ 3 } x+8=5(3)^{ 2 }-\left( \frac { 2 }{ 3 } \times 3 \right) +8=\left( 5\times 9 \right) -2+8=45-2+8=53-2=51
Hence,
p(3)=51
.
\alpha, \beta, \gamma
be the zeroes of the expression
ax^{3} + bx^{2} + 4x + 7
, then the value of
\alpha\beta + \beta\gamma + \gamma\alpha
is:
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-4
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\frac{4}{\alpha}
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-\frac{4}{\alpha}
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None of these
If
p(x) = 1 + 7x - 9x^2 + \dfrac{2}{3} x^3
, then
p(-3) =
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-81
0%
-137
0%
-119
0%
-100
Explanation
Consider the polynomial
p(x)=1+7x-9x^{ 2 }+\frac { 2 }{ 3 } x^{ 3 }
and substitute
x=-3
in the polynomial:
p(-3)=1+(7\times -3)-9(-3)^{ 2 }+\frac { 2 }{ 3 } (-3)^{ 3 }=1-21-(9\times 9)+\left( \frac { 2 }{ 3 } \times -27 \right) =1-21-81-18=-119
Hence,
p(-3)=-119
.
Calculate the number of real numbers
k
such that
f(k)=2
if
f(x)={ x }^{ 4 }-3{ x }^{ 3 }-9{ x }^{ 2 }+4
.
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None
0%
One
0%
Two
0%
Three
0%
Four
Explanation
Given,
f(x)=x^4-3x^3-9x^2+4, f(k)=2
Therefore,
y = 2= f(x)
\Rightarrow 2=x^4-3x^3-9x^2+4
\Rightarrow x^4-3x^3-9x^2+2=0
Then plug in consecutive numbers for
x
and if the sign of
f(x)
changes,
f(-2) = 6
f(-1) = -3
so there's one
f(0) = 2
so that's two
f(1 ) = -9
so that's three
And eventually it has to become positive again so there are four.
If
f(x)=x^{6}-10x^{5}-10x^{4}-10x^{3}-10x^{2}-10x+10
, the value of
f(11)
is
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1
0%
10
0%
11
0%
21
Explanation
The given expression
f(x)=x^6-10x^5-10x^4-10x^3-10x^2-10x+10
can be rewritten as
f(x)=x^{ 6 }-10(x^{ 5 }+x^{ 4 }+x^{ 3 }+x^{ 2 }+x-1)
.
Now, substitute
x=11
in the above expression as shown below:
\Rightarrow f(x)=x^{ 6 }-10(x^{ 5 }+x^{ 4 }+x^{ 3 }+x^{ 2 }+x-1)
\Rightarrow f(11)=11^{ 6 }-10(11^{ 5 }+11^{ 4 }+11^{ 3 }+11^{ 2 }+11-1)
\Rightarrow f(11)=1771561-10(161051+14641+1331+121+11-1)
\Rightarrow f(11)=1771561-(10\times 177154)
\Rightarrow f(11)=1771561-1771540
\Rightarrow f(11)=21
Hence,
f(11)=21
.
Two roots of the equation
4x^3 - px^2+ qx - 2p = 0
are 4 andWhat is the third root?
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\frac{11}{27}
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\frac{11}{13}
0%
11
0%
\frac{11}{15}
0%
-\frac{22}{27}
The equation
8x^{6} + 72x^{5} + bx^{4} + cx^{3} - 687x^{2} - 2160x - 1700 = 0
, as shown in the figure, has two complex roots. The product of these complex roots is
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-4
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\dfrac {17}{2}
0%
9
0%
\dfrac {-687}{2}
0%
\dfrac {427}{2}
Let\,x = \sqrt {3 - \sqrt 5 } \,and\,y = \sqrt {3 + \sqrt 5 } .
If the value of expression
x - y + 2{x^2}y + 2x{y^2} - {x^4}y + x{y^4}
can be expressed in the form
\sqrt p + \sqrt q
where\,p,\,q \in N,
then
(p+q)
has the value equal
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0%
448
0%
610
0%
510
0%
540
Explanation
The zeros of the polynomial
{ x }^{ 2 }-9
are
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3,3
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\sqrt { 3 } ,-\sqrt { 3 }
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3,-3
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-\sqrt { 3 } ,-\sqrt { 3 }
Number of root of equation
3|x|-|2-x|=1
is
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0
0%
2
0%
4
0%
7
The number of polynomials having zeroes as
-2
and
5
is?
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0
0%
2
0%
3
0%
More than
3
If a + b + 2 c = 0,
c\neq 0
, then equation $$
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At least one root in (0, 1)
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At least one root in (0, 2)
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At least one root in (-1, 1)
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None of these
The roots of the equation
\left( x-1 \right) ^{ 3 }+8=0
are
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-1,1+2\omega ,1+{ 2\omega }^{ 2 }
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-1,1-2\omega ,1-{ 2\omega }^{ 2 }
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2,2\omega ,{ 2\omega }^{ 2 }
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2,1+2\omega ,1+{ 2\omega }^{ 2 }
Number of common roots of the equation
x^4+x^2+1=0
and
x^8-1=0
is
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zero
0%
1
0%
2
0%
4
For equation
{ x }^{ 3 }-{ 6x }^{ 2 }+9x+k=0
to have exactly one root in (1, 3), the set of values of k is
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(-4, 0)
0%
(1, 3)
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(0, 4)
0%
None of these
If the sum of two roots of the equation
{ x }^{ 3 }-p{ x }^{ 2 }+qx-r=0
is zero, then
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pq=r
0%
qr=p
0%
pr=q
0%
pqr=1
Let
f ( x )
be a polynomial of degree 5 with leading coefficient unity, such that
f ( 1 ) = 5 , f ( 2 ) = 4 , f ( 3 ) = 3 , f ( 4 ) = 2
and
f ( 5 ) = 1 ,
then
Sum of the roots of
f ( x )
is equal to:
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0%
15
0%
-15
0%
21
0%
Can't be determine
Let
f ( x )
be a polynomial of degree 5 with leading coefficient unity, such that
f ( 1 ) = 5 , f ( 2 ) = 4 , f ( 3 ) = 3 , f ( 4 ) = 2
and
f ( 5 ) = 1 ,
then
Product of the roots of
f ( x )
is equal to:
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0%
120
0%
-120
0%
114
0%
-114
Let for
a \neq a_1 \neq 0, f(x) = ax^2 +bx +c, g(x) = a_1x^2 +b_1x+c_1
and
p(x) =f(x) -g(x)
. If
p(x) =0
only for
x= -1
and
p(-2) =2
then the value of
p(2)
is
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0%
18
0%
3
0%
9
0%
6
Let
f ( x )
be a polynomial of degree 5 with leading coefficient unity, such that
f ( 1 ) = 5 , f ( 2 ) = 4 , f ( 3 ) = 3 , f ( 4 ) = 2
and
f ( 5 ) = 1 ,
then
f ( 6 )
is equal to:
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0%
120
0%
-120
0%
0
0%
6
The product of the zero of the polynomal
{ x }^{ 2 }-4x+3
is ....
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4
0%
1
0%
-4
0%
3
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Answered
1
Not Answered
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Incorrect : 0
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