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Recent questions tagged polynomials
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1
Combinatorics : Multinomial Coefficients
What's the relationship between combination and polynomial equation? I mean, I am not able to grasp certain points here or let's say connect them into a whole: 1. Take a question where it's asked that we have to arrange 10 ... way of doing probability's tricky questions. EDIT: Here's the images of different questions. How do I differentiate between them?
asked
Jun 24, 2017
in
Combinatory
by
Vasu Srivastava
Junior
(
703
points)

243
views
permutationsandcombinations
discretemathematics
engineeringmathematics
polynomials
+2
votes
1
answer
2
ISI 2004 MIII
Q10 The equation $p\left ( x \right ) = \alpha$ where $p\left ( x \right ) = x^{4}+4x^{3}2x^{2}12x$ has four distinct real root if and only if A) $p\left ( 3 \right )<\alpha$ B) $p\left ( 1 \right )>\alpha$ C) $p\left ( 1 \right )<\alpha$ D) $p\left ( 3 \right )<\alpha <p\left ( 1 \right )$
asked
Apr 3, 2017
in
Set Theory & Algebra
by
Tesla!
Boss
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18.2k
points)

65
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isi2004
polynomials
+5
votes
2
answers
3
ISI2004MIII
The equation $\frac{1}{3}+\frac{1}{2}s^{2}+\frac{1}{6}s^{3}=s$ has exactly three solution in $[0.1]$ exactly one solution in $[0,1]$ exactly two solution in $[0,1]$ no solution in $[0,1]$
asked
Apr 3, 2017
in
Set Theory & Algebra
by
Tesla!
Boss
(
18.2k
points)

163
views
isi2004
polynomials
+1
vote
1
answer
4
ISI 2004 MIII
Q8 If $\alpha 1,\alpha 2,\alpha 3....\alpha n$ be the roots of $x^{n}+1=0$, then $\left ( 1\alpha 1 \right )*\left ( 1\alpha 2 \right )...\left ( 1\alpha n \right )$ is equal to A) 1 B) 0 C) n D) 2
asked
Apr 3, 2017
in
Set Theory & Algebra
by
Tesla!
Boss
(
18.2k
points)

47
views
isi2004
polynomials
+4
votes
2
answers
5
ISI2004MIII7
The equation $x^{6}5x^{4}+16x^{2}72x+9=0$ has exactly two distinct real roots exactly three distinct real roots exactly four distinct real roots six different real roots
asked
Apr 3, 2017
in
Set Theory & Algebra
by
Tesla!
Boss
(
18.2k
points)

316
views
isi2004
polynomials
maximaminima
+1
vote
1
answer
6
ISI 2004 MIII
Q6 If the equation $x^{4}+ax^{3}+bx^{2}+cx+1=0$ (where a,b,c are real number) has no real roots and if at least one of the root is of modulus one, then A) b=c B) a=c C) a=b D) none of this
asked
Apr 3, 2017
in
Set Theory & Algebra
by
Tesla!
Boss
(
18.2k
points)

49
views
isi2004
polynomials
+21
votes
5
answers
7
GATE2017224
Consider the quadratic equation $x^213x+36=0$ with coefficients in a base $b$. The solutions of this equation in the same base $b$ are $x=5$ and $x=6$. Then $b$= _____
asked
Feb 14, 2017
in
Set Theory & Algebra
by
khushtak
Loyal
(
7.7k
points)

3.8k
views
gate20172
polynomials
numericalanswers
+7
votes
3
answers
8
GATE19871xxii
The equation $7x^{7}+14x^{6}+12x^{5}+3x^{4}+12x^{3}+10x^{2}+5x+7=0$ has All complex roots At least one real root Four pairs of imaginary roots None of the above
asked
Nov 9, 2016
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
41.1k
points)

382
views
gate1987
polynomials
+4
votes
2
answers
9
ISRO200948
The cubic polynomial $y(x)$ which takes the following values: $y(0)=1, y(1)=0, y(2)=1$ and $y(3)=10$ is $x^3 +2x^2 +1$ $x^3 +3x^2 1$ $x^3 +1$ $x^3 2x^2 +1$
asked
Jun 15, 2016
in
Numerical Methods
by
jothee
Veteran
(
115k
points)

921
views
isro2009
polynomials
+13
votes
2
answers
10
GATE20161GA09
If $f(x) = 2x^{7}+3x5$, which of the following is a factor of $f(x)$? $\left(x^{3}+8\right)$ $(x  1)$ $(2x  5)$ $(x + 1)$
asked
Feb 12, 2016
in
Numerical Ability
by
Sandeep Singh
Loyal
(
7.8k
points)

1.3k
views
gate20161
numericalability
polynomials
normal
0
votes
1
answer
11
Mock Test 2016 GA
asked
Jan 14, 2016
in
Numerical Ability
by
bahirNaik
Active
(
3.3k
points)

147
views
testseries
numericalability
polynomials
+1
vote
0
answers
12
TIFR2014MathsB6
The number of irreducible polynomials of the form $x^{2}+ax+b$, with $a, b$ in the field $\mathbb{F}_{7}$ of $7$ elements is: 7 21 35 49.
asked
Dec 17, 2015
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
41.1k
points)

52
views
tifrmaths2014
polynomials
nongate
+1
vote
1
answer
13
TIFR2011MathsB9
Let $P$ be a degree $3$ polynomial with complex coefficients such that the constant term is $2010$. Then $P$ has a root $\alpha$ with $\alpha > 10$.
asked
Dec 10, 2015
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
41.1k
points)

88
views
tifrmaths2011
polynomials
+1
vote
2
answers
14
TIFR2011MathsA16
The polynomial $x^{4}+7x^{3}13x^{2}+11x$ has exactly one real root.
asked
Dec 9, 2015
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
41.1k
points)

124
views
tifrmaths2011
polynomials
+1
vote
1
answer
15
TIFR2011MathsA11
For any real number $c$, the polynomial $x^{3}+x+c$ has exactly one real root.
asked
Dec 9, 2015
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
41.1k
points)

93
views
tifrmaths2011
polynomials
+1
vote
1
answer
16
TIFR2011MathsA8
The sum of the squares of the roots of the cubic equation $x^{3}4x^{2}+6x+1$ is 0. 4. 16. none of the above.
asked
Dec 9, 2015
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
41.1k
points)

98
views
tifrmaths2011
polynomials
+3
votes
0
answers
17
TIFR2010MathsB15
Which of the following statements is false? The polynomial $x^{2}+x+1$ is irreducible in $\mathbb{Z}/2\mathbb{Z}[x]$. The polynomial $x^{2}2$ is irreducible in $\mathbb{Q}[x]$. The polynomial $x^{2}+1$ is reducible in $\mathbb{Z}/5\mathbb{Z}[x]$. The polynomial $x^{2}+1$ is reducible in $\mathbb{Z}/7\mathbb{Z}[x]$.
asked
Nov 14, 2015
in
Set Theory & Algebra
by
Arjun
Veteran
(
395k
points)

157
views
tifrmaths2010
polynomials
+7
votes
2
answers
18
TIFR2012A12
For the polynomial $p(x)= 8x^{10}7x^{3}+x1$ consider the following statements (which may be true or false) It has a root between $[0, 1].$ It has a root between $[0, 1].$ It has no roots outside $(1, 1).$ Which of the above statements are true? Only (i). Only (i) and (ii). Only (i) and (iii). Only (ii) and (iii). All of (i), (ii) and (iii).
asked
Oct 30, 2015
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
41.1k
points)

412
views
tifr2012
settheory&algebra
polynomials
+1
vote
1
answer
19
Factor of determinant with identical row
How the following fact applies to determinants (I came across it while solving problems): Consider A is a n× n matrix, the elements of which are real (or complex) polynomials in x. If r rows of the determinant become identical when x ... is collapsing of rows of matrix (into one row) with order of its factors. Am I missing some stupid fact here?
asked
Dec 3, 2014
in
Linear Algebra
by
Mahesha999
Junior
(
541
points)

693
views
matrices
linearalgebra
polynomials
+12
votes
2
answers
20
GATE19952.8
If the cube roots of unity are $1, \omega$ and $\omega^2$, then the roots of the following equation are $(x1)^3 +8 =0$ $1, 1 + 2\omega, 1 + 2\omega^2$ $1, 1  2\omega, 1  2\omega^2$ $1, 1  2\omega, 1  2\omega^2$ $1, 1 + 2\omega, 1 + 2\omega^2$
asked
Oct 8, 2014
in
Set Theory & Algebra
by
Kathleen
Veteran
(
59.8k
points)

659
views
gate1995
settheory&algebra
normal
polynomials
+17
votes
3
answers
21
GATE19974.4
A polynomial $p(x)$ is such that $p(0) = 5, p(1) = 4, p(2) = 9$ and $p(3) = 20$. The minimum degree it should have is $1$ $2$ $3$ $4$
asked
Sep 29, 2014
in
Set Theory & Algebra
by
Kathleen
Veteran
(
59.8k
points)

1.8k
views
gate1997
settheory&algebra
normal
polynomials
+17
votes
3
answers
22
GATE201425
A nonzero polynomial $f(x)$ of degree 3 has roots at $x=1$, $x=2$ and $x=3$. Which one of the following must be TRUE? $f(0)f(4)< 0$ $f(0)f(4)> 0$ $f(0)+f(4)> 0$ $f(0)+f(4)< 0$
asked
Sep 28, 2014
in
Set Theory & Algebra
by
jothee
Veteran
(
115k
points)

1.4k
views
gate20142
settheory&algebra
polynomials
normal
+24
votes
4
answers
23
GATE20002.4
A polynomial $p(x)$ satisfies the following: $p(1) = p(3) = p(5) = 1$ $p(2) = p(4) = 1$ The minimum degree of such a polynomial is $1$ $2$ $3$ $4$
asked
Sep 14, 2014
in
Set Theory & Algebra
by
Kathleen
Veteran
(
59.8k
points)

2k
views
gate2000
settheory&algebra
normal
polynomials
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