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1

GATE CH 2023 | GA Question: 9
The coefficient of $x^{4}$ in the polynomial $(x-1)^{3}(x-2)^{3}$ is equal to___________. $33$ $-3$ $30$ $21$

admin asked in Quantitative Aptitude May 21, 2023

by admin

896 views

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2

Best Open Video Playlist for Polynomials Topic | Quantitative Aptitude
Please list out the best free available video playlist for Polynomials from Quantitative Aptitude as an answer here (only one playlist per answer). We'll then select the best playlist and add to GO classroom video lists. ... ones are more likely to be selected as best. For the full list of selected videos please see here

makhdoom ghaya asked in Study Resources Aug 26, 2022

by makhdoom ghaya

115 views

3 votes

1 answer

3

NIELIT 2016 MAR Scientist B - Section C: 21
A polynomial $p(x)$ is such that $p(0)=5, \: p(1)=4, \: p(2)=9$ and $p(3)=20$. The minimum degree it can have is $1$ $2$ $3$ $4$

admin asked in Set Theory & Algebra Mar 31, 2020

by admin

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4

Michael Sipser Edition 3 Exercise 3 Question 21 (Page No. 190)
Let $c_{1}x^{n} + c_{2}x^{n-1} + \dots + c_{n}x + c_{n+1}$ be a polynomial with a root at $x = x_{0}.$ Let $c_{max}$ be the largest absolute value of a $c_{i}.$ Show that $\mid x_{0} \mid < (n+1)\frac{c_{max}}{\mid c_{1} \mid}.$

admin asked in Theory of Computation Oct 15, 2019

by admin

157 views

1 vote

1 answer

5

ISI2015-MMA-12
Consider the polynomial $x^5+ax^4+bx^3+cx^2+dx+4$ where $a,b,c,d$ are real numbers. If $(1+2i)$ and $(3-2i)$ are two two roots of this polynomial then the value of $a$ is $-524/65$ $524/65$ $-1/65$ $1/65$

Arjun asked in Quantitative Aptitude Sep 23, 2019

by Arjun

743 views

1 vote

1 answer

6

ISI2018-DCG-10
Let $f’(x)=4x^3-3x^2+2x+k,$ $f(0)=1$ and $f(1)=4.$ Then $f(x)$ is equal to $4x^4-3x^3+2x^2+x+1$ $x^4-x^3+x^2+2x+1$ $x^4-x^3+x^2+2(x+1)$ none of these

gatecse asked in Calculus Sep 18, 2019

370 views

1 vote

0 answers

7

ISI2018-DCG-11
The sum of $99^{th}$ power of all the roots of $x^7-1=0$ is equal to $1$ $2$ $-1$ $0$

gatecse asked in Quantitative Aptitude Sep 18, 2019

383 views

5 votes

2 answers

8

GATE2018 EE: GA-3
The three roots of the equation $f(x) = 0$ are $x = \{−2, 0, 3\}$. What are the three values of $x$ for which $f(x − 3) = 0?$ $−5, −3, 0$ $−2, 0, 3$ $0, 6, 8$ $1, 3, 6$

Lakshman Bhaiya asked in Quantitative Aptitude Feb 20, 2018

by Lakshman Bhaiya

2.0k views

4 votes

2 answers

9

GATE2018 CH: GA-9
If $x^{2}+ x - 1 = 0$ what is the value of $x^4 + \dfrac{1}{x^4}$? $1$ $5$ $7$ $9$

Lakshman Bhaiya asked in Quantitative Aptitude Feb 20, 2018

by Lakshman Bhaiya

1.1k views

1 vote

0 answers

10

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 ... doing probability's tricky questions. EDIT: Here's the images of different questions. How do I differentiate between them?

Vasu Srivastava asked in Combinatory Jun 23, 2017

by Vasu Srivastava

936 views

2 votes

1 answer

11

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 $p\left ( -3 \right )<\alpha$ $p\left ( -1 \right )>\alpha$ $p\left ( -1 \right )<\alpha$ $p\left ( -3 \right )<\alpha <p\left ( -1 \right )$

Tesla! asked in Set Theory & Algebra Apr 3, 2017

by Tesla!

502 views

6 votes

2 answers

12

ISI2004-MIII
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 $[0,1]$

Tesla! asked in Set Theory & Algebra Apr 3, 2017

by Tesla!

635 views

2 votes

1 answer

13

ISI 2004 MIII
$Q8$ If $\alpha_{1},\alpha_{2},\alpha_{3}, \dots , \alpha_{n}$ be the roots of $x^{n}+1=0$, then $\left ( 1-\alpha_{1} \right )\left ( 1-\alpha_{2} \right ) \dots \left ( 1-\alpha_{n} \right )$ is equal to $1$ $0$ $n$ $2$

Tesla! asked in Set Theory & Algebra Apr 3, 2017

by Tesla!

446 views

5 votes

2 answers

14

ISI2004-MIII: 7
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

Tesla! asked in Set Theory & Algebra Apr 3, 2017

by Tesla!

1.8k views

1 vote

1 answer

15

ISI 2004 MIII
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 $b=c$ $a=c$ $a=b$ none of this

Tesla! asked in Set Theory & Algebra Apr 3, 2017

by Tesla!

356 views

39 votes

5 answers

16

GATE CSE 2017 Set 2 | Question: 24
Consider the quadratic equation $x^2-13x+36=0$ with coefficients in a base $b$. The solutions of this equation in the same base $b$ are $x=5$ and $x=6$. Then $b=$ _____

khushtak asked in Set Theory & Algebra Feb 14, 2017

14.3k views

15 votes

5 answers

17

GATE CSE 1987 | Question: 1-xxii
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

makhdoom ghaya asked in Calculus Nov 8, 2016

by makhdoom ghaya

2.8k views

4 votes

2 answers

18

ISRO2009-48
The cubic polynomial $y(x)$ which takes the following values: $y(0)=1, y(1)=0, y(2)=1$ and $y(3)=10$ is $x^3 +2x^2 +1$ $x^3 +3x^2 -1$ $x^3 +1$ $x^3 -2x^2 +1$

go_editor asked in Numerical Methods Jun 15, 2016

1.9k views

20 votes

2 answers

19

GATE CSE 2016 Set 1 | Question: GA09
If $f(x) = 2x^{7}+3x-5$, which of the following is a factor of $f(x)$? $\left(x^{3}+8\right)$ $(x - 1)$ $(2x - 5)$ $(x + 1)$

Sandeep Singh asked in Quantitative Aptitude Feb 12, 2016

by Sandeep Singh

4.3k views

0 votes

1 answer

20

Mock Test 2016 GA

bahirNaik asked in Quantitative Aptitude Jan 14, 2016

406 views

2 votes

0 answers

21

TIFR-2014-Maths-B-6
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

makhdoom ghaya asked in Set Theory & Algebra Dec 17, 2015

by makhdoom ghaya

348 views

1 vote

1 answer

22

TIFR-2011-Maths-B-9
Let $P$ be a degree $3$ polynomial with complex coefficients such that the constant term is $2010$. Then $P$ has a root $\alpha$ with $|\alpha| > 10$.

makhdoom ghaya asked in Set Theory & Algebra Dec 10, 2015

by makhdoom ghaya

508 views

1 vote

2 answers

23

TIFR-2011-Maths-A-16
The polynomial $x^{4}+7x^{3}-13x^{2}+11x$ has exactly one real root.

makhdoom ghaya asked in Set Theory & Algebra Dec 9, 2015

by makhdoom ghaya

700 views

2 votes

1 answer

24

TIFR-2011-Maths-A-11
For any real number $c$, the polynomial $x^{3}+x+c$ has exactly one real root.

makhdoom ghaya asked in Set Theory & Algebra Dec 9, 2015

by makhdoom ghaya

410 views

1 vote

1 answer

25

TIFR-2011-Maths-A-8
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

makhdoom ghaya asked in Set Theory & Algebra Dec 9, 2015

by makhdoom ghaya

1.3k views

2 votes

1 answer

26

Algorithm
A polynomial p(x) is such that p(0)=5 ,p(1)=4 ,p(2)=9 and p(3)=20 The minimum degree it can have is..

Soumyashree asked in Calculus Nov 21, 2015

460 views

4 votes

0 answers

27

TIFR2010-Maths-B-15
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 $\mathbb{Z}/7\mathbb{Z}[x]$.

Arjun asked in Set Theory & Algebra Nov 14, 2015

by Arjun

603 views

3 votes

1 answer

28

TIFR CSE 2013 | Part B | Question: 2
Consider polynomials in a single variable $x$ of degree $d$. Suppose $d < n/2$. For such a polynomial $p(x)$, let $C_{p}$ denote the $n$-tuple $(P\left ( i \right ))_{1 \leq i \leq n}$. For any two such distinct polynomials $p, q,$ the number of ... $d$ At most $n - d$ Between $d$ and $n - d$ At least $n - d$ None of the above.

makhdoom ghaya asked in Quantitative Aptitude Nov 6, 2015

by makhdoom ghaya

641 views

15 votes

2 answers

29

TIFR CSE 2012 | Part A | Question: 12
For the polynomial $p(x)= 8x^{10}-7x^{3}+x-1$ 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).

makhdoom ghaya asked in Calculus Oct 30, 2015

by makhdoom ghaya

1.4k views

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Recent questions tagged polynomials