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Recent questions tagged polynomials

4 votes
1 answer
1
GATE CH 2023 | GA Question: 9
The coefficient of $x^{4}$ in the polynomial $(x-1)^{3}(x-2)^{3}$ is equal to___________. $33$ $-3$ $30$ $21$
The coefficient of $x^{4}$ in the polynomial $(x-1)^{3}(x-2)^{3}$ is equal to___________.$33$$-3$$30$$21$
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3 votes
1 answer
3
NIELIT 2016 MAR Scientist B - Section C: 21
A polynomial $p(x)$ is such that $p(0)=5, \: p(1)=4, \: p(2)=9$ and $p(3)=20$. The minimum degree it can have is $1$ $2$ $3$ $4$
A polynomial $p(x)$ is such that $p(0)=5, \: p(1)=4, \: p(2)=9$ and $p(3)=20$. The minimum degree it can have is$1$$2$$3$$4$
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1 votes
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 $-524/65$ $524/65$ $-1/65$ $1/65$
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 $a$ i...
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1 votes
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
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
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1 votes
0 answers
7
ISI2018-DCG-11
The sum of $99^{th}$ power of all the roots of $x^7-1=0$ is equal to $1$ $2$ $-1$ $0$
The sum of $99^{th}$ power of all the roots of $x^7-1=0$ is equal to$1$$2$$-1$$0$
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5 votes
2 answers
8
GATE2018 EE: GA-3
The three roots of the equation $f(x) = 0$ are $x = \{−2, 0, 3\}$. What are the three values of $x$ for which $f(x − 3) = 0?$ $−5, −3, 0$ $−2, 0, 3$ $0, 6, 8$ $1, 3, 6$
The three roots of the equation $f(x) = 0$ are $x = \{−2, 0, 3\}$. What are the three values of $x$ for which $f(x − 3) = 0?$$−5, −3, 0$$−2, 0, 3$$0, 6, 8$$1, 3...
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4 votes
2 answers
9
GATE2018 CH: GA-9
If $x^{2}+ x - 1 = 0$ what is the value of $x^4 + \dfrac{1}{x^4}$? $1$ $5$ $7$ $9$
If $x^{2}+ x - 1 = 0$ what is the value of $x^4 + \dfrac{1}{x^4}$?$1$$5$$7$$9$
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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 $[0,1]$
The equation $\frac{1}{3}+\frac{1}{2}s^{2}+\frac{1}{6}s^{3}=s$hasexactly three solution in $[0.1]$exactly one solution in $[0,1]$exactly two solution in $[0,1]$no solu...
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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 $1$ $0$ $n$ $2$
$Q8$ 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 (...
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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
The equation $x^{6}-5x^{4}+16x^{2}-72x+9=0$ hasexactly two distinct real rootsexactly three distinct real rootsexactly four distinct real rootssix different real roots
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1 votes
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
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 ...
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40 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 $b=$ _____
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 $b=$ _____
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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
The equation $7x^{7}+14x^{6}+12x^{5}+3x^{4}+12x^{3}+10x^{2}+5x+7=0$ hasAll complex rootsAt least one real rootFour pairs of imaginary rootsNone of the above
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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 $x^3 +2x^2 +1$ $x^3 +3x^2 -1$ $x^3 +1$ $x^3 -2x^2 +1$
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$$x^3 -2x^2 +1$
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20 votes
2 answers
19
GATE CSE 2016 Set 1 | Question: GA09
If $f(x) = 2x^{7}+3x-5$, which of the following is a factor of $f(x)$? $\left(x^{3}+8\right)$ $(x - 1)$ $(2x - 5)$ $(x + 1)$
If $f(x) = 2x^{7}+3x-5$, which of the following is a factor of $f(x)$?$\left(x^{3}+8\right)$$(x - 1)$$(2x - 5)$$(x + 1)$
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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
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
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1 votes
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 $|\alpha| > 10$.
Let $P$ be a degree $3$ polynomial with complex coefficients such that the constant term is $2010$. Then $P$ has a root $\alpha$ with $|\alpha| 10$.
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1 votes
2 answers
23
TIFR-2011-Maths-A-16
The polynomial $x^{4}+7x^{3}-13x^{2}+11x$ has exactly one real root.
The polynomial $x^{4}+7x^{3}-13x^{2}+11x$ has exactly one real root.
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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.
For any real number $c$, the polynomial $x^{3}+x+c$ has exactly one real root.
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1 votes
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
The sum of the squares of the roots of the cubic equation $x^{3}-4x^{2}+6x+1$ is0. 4.16. none of the above
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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..
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..
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