The roots of the equation $$ax^3 + bx^2 - x + 1=0$$ are real, distinct and are in H.P., then

$$a$$ $$\epsilon$$ $$(-\frac{1}{27},\infty)$$

$$b$$ $$\epsilon$$ $$(-\infty,\frac{1}{3})$$

The HCF of two ploynomials $$A$$ and $$B$$ using long division method was found to be $$2x + 1$$ after two steps . The fisrt two quotient obtained are $$x$$ and $$(x + 1)$$ . Find $$A$$ and $$B$$ . Given that degree of $$A$$ > degree of $$B$$ is

$$A = 2x^3 + 3x^2 + 3x + 1 $$ ; $$B = 2x^2 + 3x + 1 $$

$$A = 2x^3 + 3x^2 + x - 1 $$ ; $$B = 2x^2 - 3x + 1 $$

$$A = 2x^3 - 3x^2 + x - 1 $$ ; $$B = 2x^2 - 3x - 1 $$

$$A = 2x^3 + 3x^2 - 3x - 1 $$ ; $$B = 2x^2 - 3x + 1 $$

The root of the equation $${ X }^{ 4 }-1=0$$ are;

1,-1,$${ \omega ,\omega }^{ 2 }$$

MCQ Questions for Class 9 Maths Polynomials Quiz 13

If the sum of two roots of the equation

x^{3} p x^{2} + q x r = 0

$\displaystyle x^3 px^2 + qx r = 0$ is zero , then

0%
pq = r
0%
qr = p
0%
pr = q
0%
pqr = 1

f (x) = {4 x}^{4} - {a x}^{3} + {b x}^{2} - c x + 5

$f(x)={ 4x }^{ 4 }-{ ax }^{ 3 }+{ bx }^{ 2 }-cx+5$ (a, b, c

\in

$\in$ R) has four positive real zeros

r_{1}, r_{2}, r_{3}, r_{4}

${ r }_{ 1 },{ r }_{ 2 },{ r }_{ 3 },{ r }_{ 4 }$ such that

\frac{r_{1}}{2} + \frac{r_{2}}{4} + \frac{r_{3}}{5} + \frac{r_{4}}{8} = 1

$\frac { { r }_{ 1 } }{ 2 } +\frac { { r }_{ 2 } }{ 4 } +\frac { { r }_{ 3 } }{ 5 } +\frac { { r }_{ 4 } }{ 8 } =1$ , then a is equal to

0%
19
0%
20
0%
21
0%
22

The equation

{(x - 3)}^{9} + {(x - 3^{2})}^{9} + {(x - 3^{3})}^{9} + . . . . + {(x - 3^{9})}^{9} = 0 h a s :

${\left( {x - 3} \right)^9} + {\left( {x - {3^2}} \right)^9} + {\left( {x - {3^3}} \right)^9} + .... + {\left( {x - {3^9}} \right)^9} = 0\;has:$

0%
all the roots are real
0%
One real and 8 imaginary roots
0%
real roots namely $x = 3,\;{3^2},{.....3^9}$
0%
Five real and 4 imaginary roots

The roots of the equation

a x^{3} + b x^{2} - x + 1 = 0

$ax^3 + bx^2 - x + 1=0$ are real, distinct and are in H.P., then

0%
$b$ $\epsilon$ $(-\infty,\frac{1}{3})$
0%
$a$ $\epsilon$ $(-\frac{1}{27},\infty)$
0%
$27a + 9b=2$
0%
None of these

The roots of

6 x^{4} - 35 x^{3} + 62^{2} - 35 x + 6 = 0

$6x^{4}-35x^{3}+62^{2}-35x+6=0$ are.......

0%
2,-1/2,-1/3,3
0%
2,1/2,3,1/3
0%
-2,-1/2,-3,-1/3
0%
2,1/2,-3,-1/3

p, q, r, s \in R

$p,\quad q,\quad r,\quad s\quad \in R$ , then equation

(x^{2} + p x + 3 q) ({- x}^{2} + r x + q) ({- x}^{2} + s x - 2 q) = 0

$({ x }^{ 2 }+{ px }+{ 3 }q)({ -x }^{ 2 }+rx+q)({ -x }^{ 2 }+sx-2q)=0$ has

0%
6 real roots
0%
atleast two real roots
0%
2 real and 4 imaginary roots
0%
4 real and 2 imaginary roots

The sum of the roots of the equation

c o t - 1 x - 1 (x + 2) = 150

$cot-1x-1(x+2)=150$ is

0%
0
0%
1
0%
2
0%
-2

1, - 2, 3

$1,-2,3$ are the roots of

x^{3} - b x^{2} + a x + 6 = 0

${ x }^{ 3 }-b{ x }^{ 2 }+ax+6=0$ , then a=

0%
$-5$
0%
$5$
0%
$2$
0%
none of these

The expansion

\frac{1}{\sqrt{4 x + 1}} [{[\frac{1 + \sqrt{4 x + 1}}{2}]}^{7} - {[\frac{1 - \sqrt{4 x - 1}}{2}]}^{7}]

$\frac{1}{{\sqrt {4x + 1} }}\left[ {{{\left[ {\frac{{1 + \sqrt {4x + 1} }}{2}} \right]}^7} - {{\left[ {\frac{{1 - \sqrt {4x - 1} }}{2}} \right]}^7}} \right]$ is a polynomial in x of degree

0%
7
0%
6
0%
4
0%
3

If roots of equation

8 x^{3} - 14 x^{2} + 7 x - 1 = 0

$8x^3 -14x^2+7x-1 =0$ are in geometric progression, then roots are

0%
$3,6,8$
0%
$1,2,4$
0%
$2,4,8$
0%
$1,1/2,1/4$

a, β, y

$a,\beta ,y$ are the roots of equation

x^{3} + 2 x - 5 = 0

${ x }^{ 3 }+2x-5=0$ and if equation

x^{3} + {b x}^{2} + c x + d = 0 h a s r o o t s 2 a + 1. 2 β + 1, 2 y + 1.

${ x }^{ 3 }+{ bx }^{ 2 }+cx+d=0\quad has\quad roots\quad 2a+1.\quad 2\beta +1,\quad 2y+1.$ then value of

| b + c + d |

$\left| b+c+d \right|$ is (where b,c,dd are coprime ) -

0%
41
0%
39
0%
40
0%
43

The expression

{[x + {(x^{3} - 1)}^{1 / 2}]}^{5} + {[x - {(x^{3} - 1)}^{1 / 2}]}^{5}

${ \left[ x+{ \left( { x }^{ 3 }-1 \right) }^{ 1/2 } \right] }^{ 5 }+{ \left[ x-{ \left( { x }^{ 3 }-1 \right) }^{ 1/2 } \right] }^{ 5 }$ is a polynomial of degree

0%
5
0%
6
0%
7
0%
8

If a is a non-real root of

x^{6} = 1

${ x }^{ 6 }=1$ , then

\frac{a^{5} a^{3} + a + 1}{a^{2} + 1}

$\dfrac { { a }^{ 5 }{ a }^{ 3 }+a+1 }{ { a }^{ 2 }+1 }$ is

0%
${ a }^{ 2 }$
0%
0
0%
${ -a }^{ 2 }$
0%
a

If one root of

32 x^{3} - 48 x^{2} + 22 x - 3 = 0

$32 x ^ { 3 } - 48 x ^ { 2 } + 22 x - 3 = 0$ is equal to half of the sum of the other two roots , then the roots are

0%
$1 / 4,1 / 2,3 / 4$
0%
$4,2,4 / 3$
0%
$3,4,5$
0%
$2.3 .5/2$

The expression

(x + (x^{4} - 1)^{1 / 2})^{4} + (x - (x^{4} - 1)^{1 / 2})^{4}

$(x+(x^4-1)^{1/2})^4 + (x-(x^4-1)^{1/2})^4$ is a polynomial of degree

0%
8
0%
6
0%
4
0%
2

number of real roots of the equation

\sqrt{x} + \sqrt{x - \sqrt{1 - x}} = 1 i s

$\sqrt { x } +\sqrt { x-\sqrt { 1-x } } =1\quad is$

0%
0
0%
1
0%
2
0%
3

Find the value of

\frac{10.5 \times 10.5 - 15 \times 10.5 + 7.5 \times 7.5}{10.5 - 7.5} .

$\dfrac { 10.5 \times 10.5 - 15 \times 10.5 + 7.5 \times 7.5 } { 10.5 - 7.5 }.$

0%
$17$
0%
$3$
0%
$6$
0%
$22$

α, β, γ

$\alpha ,\beta ,\gamma$ are roots of

7 x^{3} - x - 2 = 0

$7{ x }^{ 3 }-x-2=0$ then find the value of

\sum (\frac{α}{β} + \frac{β}{α})

$\sum { \left( \dfrac { \alpha }{ \beta } +\dfrac { \beta }{ \alpha } \right) }$

0%
1
0%
2
0%
-3
0%
-4

The HCF of two ploynomials

A

$A$ and

B

$B$ using long division method was found to be

2 x + 1

$2x + 1$ after two steps . The fisrt two quotient obtained are

x

$x$ and

(x + 1)

$(x + 1)$ . Find

A

$A$ and

B

$B$ . Given that degree of

A

$A$ > degree of

B

$B$ is

0%
$A = 2x^3 + 3x^2 + x - 1$ ; $B = 2x^2 - 3x + 1$
0%
$A = 2x^3 - 3x^2 + x - 1$ ; $B = 2x^2 - 3x - 1$
0%
$A = 2x^3 + 3x^2 - 3x - 1$ ; $B = 2x^2 - 3x + 1$
0%
$A = 2x^3 + 3x^2 + 3x + 1$ ; $B = 2x^2 + 3x + 1$

The degree of the expression

(1 + x) (1 + x^{6}) (1 + x^{11}) . . . . . . . . (1 + x^{101})

$(1+x)(1+{ x }^{ 6 })(1+{ x }^{ 11 })........(1+{ x }^{ 101 })$
is

0%
1081
0%
1061
0%
1071
0%
1091

The root of the equation

X^{4} - 1 = 0

${ X }^{ 4 }-1=0$ are;

0%
1,1,i,-i
0%
1,-1,i,-i
0%
1,-1, ${ \omega ,\omega }^{ 2 }$
0%
none of these

The expression

\frac{1}{\sqrt{4 x + 1}} [{[\frac{1 + \sqrt{4 x + 1}}{2}]}^{7} - {[\frac{1 - \sqrt{4 x + 1}}{2}]}^{7}]

$\frac { 1 }{ \sqrt { 4x+1 } } \left[ \left[ \dfrac { 1+\sqrt { 4x+1 } }{ 2 } \right] ^{ 7 }-\left[ \dfrac { 1-\sqrt { 4x+1 } }{ 2 } \right] ^{ 7 } \right]$ is a polynomial in x degree-

0%
7
0%
5
0%
4
0%
3

CBSE Questions for Class 9 Maths Polynomials Quiz 13 - MCQExams.com

0:0:2

Practice Class 9 Maths Quiz Questions and Answers

CBSE Questions for Class 9 Maths Polynomials Quiz 13 - MCQExams.com

0:0:2

Practice Class 9 Maths Quiz Questions and Answers

Support mcqexams.com by disabling your adblocker.