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Recent questions tagged roots
2
votes
1
answer
1
ISI2014-DCG-30
Consider the equation $P(x) =x^3+px^2+qx+r=0$ where $p,q$ and $r$ are all real and positive. State which of the following statements is always correct. All roots of $P(x) = 0$ are real The equation $P(x)=0$ has at least one real root The equation $P(x)=0$ has no negative real root The equation $P(x)=0$ must have one positive and one negative real root
Arjun
asked
in
Quantitative Aptitude
Sep 23, 2019
by
Arjun
410
views
isi2014-dcg
quantitative-aptitude
quadratic-equations
roots
1
vote
1
answer
2
ISI2014-DCG-54
The number of real roots of the equation $1+\cos ^2x+\cos ^3 x – \cos^4x=5$ is equal to $0$ $1$ $3$ $4$
Arjun
asked
in
Quantitative Aptitude
Sep 23, 2019
by
Arjun
554
views
isi2014-dcg
quantitative-aptitude
trigonometry
roots
1
vote
1
answer
3
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
748
views
isi2015-mma
quantitative-aptitude
number-system
polynomials
roots
non-gate
0
votes
1
answer
4
ISI2015-DCG-7
Let $x^2-2(4k-1)x+15k^2-2k-7>0$ for any real value of $x$. Then the integer value of $k$ is $2$ $4$ $3$ $1$
gatecse
asked
in
Quantitative Aptitude
Sep 18, 2019
by
gatecse
542
views
isi2015-dcg
quantitative-aptitude
quadratic-equations
roots
1
vote
1
answer
5
ISI2015-DCG-25
If $\alpha$ and $\beta$ be the roots of the equation $x^2+3x+4=0$, then the equation with roots $(\alpha + \beta)^2$ and $(\alpha – \beta)^2$ is $x^2+2x+63=0$ $x^2-63x+2=0$ $x^2-2x-63=0$ None of the above
gatecse
asked
in
Quantitative Aptitude
Sep 18, 2019
by
gatecse
462
views
isi2015-dcg
quantitative-aptitude
quadratic-equations
roots
0
votes
1
answer
6
ISI2015-DCG-26
If $r$ be the ratio of the roots of the equation $ax^{2}+bx+c=0,$ then $\frac{r}{b}=\frac{r+1}{ac}$ $\frac{r+1}{b}=\frac{r}{ac}$ $\frac{(r+1)^{2}}{r}=\frac{b^{2}}{ac}$ $\left(\frac{r}{b}\right)^{2}=\frac{r+1}{ac}$
gatecse
asked
in
Quantitative Aptitude
Sep 18, 2019
by
gatecse
245
views
isi2015-dcg
quantitative-aptitude
quadratic-equations
roots
0
votes
1
answer
7
ISI2015-DCG-28
If one root of a quadratic equation $ax^2+bx+c=0$ be equal to the $n^{th}$ power of the other, then $(ac)^{\frac{n}{n+1}} +b=0$ $(ac)^{\frac{n+1}{n}} +b=0$ $(ac^{n})^{\frac{1}{n+1}} +(a^nc)^{\frac{1}{n+1}}+b=0$ $(ac^{\frac{1}{n+1}})^n +(a^{\frac{1}{n+1}}c)^{n+1}+b=0$
gatecse
asked
in
Quantitative Aptitude
Sep 18, 2019
by
gatecse
258
views
isi2015-dcg
quantitative-aptitude
quadratic-equations
roots
0
votes
1
answer
8
ISI2015-DCG-30
Let $p,q,r,s$ be real numbers such that $pr=2(q+s)$. Consider the equations $x^2+px+q=0$ and $x^2+rx+s=0$. Then at least one of the equations has real roots both these equations have real roots neither of these equations have real roots given data is not sufficient to arrive at any conclusion
gatecse
asked
in
Quantitative Aptitude
Sep 18, 2019
by
gatecse
372
views
isi2015-dcg
quantitative-aptitude
quadratic-equations
roots
0
votes
1
answer
9
ISI2016-DCG-7
Let $x^{2}-2(4k-1)x+15k^{2}-2k-7>0$ for any real value of $x$. Then the integer value of $k$ is $2$ $4$ $3$ $1$
gatecse
asked
in
Quantitative Aptitude
Sep 18, 2019
by
gatecse
259
views
isi2016-dcg
quantitative-aptitude
quadratic-equations
roots
1
vote
1
answer
10
ISI2016-DCG-25
If $\alpha$ and $\beta$ be the roots of the equation $x^{2}+3x+4=0,$ then the equation with roots $(\alpha+\beta)^{2}$ and $(\alpha-\beta)^{2}$ is $x^{2}+2x+63=0$ $x^{2}-63x+2=0$ $x^{2}-2x-63=0$ None of these
gatecse
asked
in
Quantitative Aptitude
Sep 18, 2019
by
gatecse
316
views
isi2016-dcg
quantitative-aptitude
quadratic-equations
roots
1
vote
2
answers
11
ISI2016-DCG-26
If $r$ be the ratio of the roots of the equation $ax^{2}+bx+c=0,$ then $\frac{r}{b}=\frac{r+1}{ac}$ $\frac{r+1}{b}=\frac{r}{ac}$ $\frac{(r+1)^{2}}{r}=\frac{b^{2}}{ac}$ $\left(\frac{r}{b}\right)^{2}=\frac{r+1}{ac}$
gatecse
asked
in
Quantitative Aptitude
Sep 18, 2019
by
gatecse
427
views
isi2016-dcg
quantitative-aptitude
quadratic-equations
roots
2
votes
1
answer
12
ISI2016-DCG-28
If one root of a quadratic equation $ax^{2}+bx+c=0$ be equal to the n th power of the other, then $(ac)^{\frac{n}{n+1}}+b=0$ $(ac)^{\frac{n+1}{n}}+b=0$ $(ac^{n})^{\frac{1}{n+1}}+(a^{n}c)^{\frac{1}{n+1}}+b=0$ $(ac^\frac{1}{n+1})^{n}+(a^\frac{1}{n+1}c)^{n+1}+b=0$
gatecse
asked
in
Quantitative Aptitude
Sep 18, 2019
by
gatecse
604
views
isi2016-dcg
quantitative-aptitude
quadratic-equations
roots
1
vote
0
answers
13
ISI2016-DCG-29
The condition that ensures that the roots of the equation $x^{3}-px^{2}+qx-r=0$ are in H.P. is $r^{2}-9pqr+q^{3}=0$ $27r^{2}-9pqr+3q^{3}=0$ $3r^{3}-27pqr-9q^{3}=0$ $27r^{2}-9pqr+2q^{3}=0$
gatecse
asked
in
Quantitative Aptitude
Sep 18, 2019
by
gatecse
228
views
isi2016-dcg
quantitative-aptitude
quadratic-equations
roots
0
votes
1
answer
14
ISI2016-DCG-30
Let $p,q,r,s$ be real numbers such that $pr=2(q+s).$ Consider the equations $x^{2}+px+q=0$ and $x^{2}+rx+s=0.$ Then at least one of the equations has real roots. both these equations have real roots. neither of these equations have real roots. given data is not sufficient to arrive at any conclusion.
gatecse
asked
in
Quantitative Aptitude
Sep 18, 2019
by
gatecse
375
views
isi2016-dcg
quantitative-aptitude
quadratic-equations
roots
0
votes
1
answer
15
ISI2017-DCG-5
The sum of the squares of the roots of $x^2-(a-2)x-a-1=0$ becomes minimum when $a$ is $0$ $1$ $2$ $5$
gatecse
asked
in
Quantitative Aptitude
Sep 18, 2019
by
gatecse
344
views
isi2017-dcg
quantitative-aptitude
quadratic-equations
roots
1
vote
0
answers
16
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
by
gatecse
385
views
isi2018-dcg
quantitative-aptitude
polynomials
roots
0
votes
1
answer
17
ISI2017-PCB-A-1
Suppose all the roots of the equation $x^3 +bx-2017=0$ (where $b$ is a real number) are real. Prove that exactly one root is positive.
go_editor
asked
in
Quantitative Aptitude
Sep 19, 2018
by
go_editor
548
views
isi2017-pcb-a
quantitative-aptitude
cubic-equations
roots
descriptive
1
vote
1
answer
18
ISI2016-PCB-A-1
If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+6x+1=0$, then prove that $\frac{\alpha}{\beta} + \frac{\beta}{\alpha} + \frac{\beta}{\gamma}+ \frac{\gamma}{\beta} + \frac{\gamma}{\alpha}+ \frac{\alpha}{\gamma}=-3.$
go_editor
asked
in
Quantitative Aptitude
Sep 18, 2018
by
go_editor
470
views
isi2016-pcb-a
quantitative-aptitude
quadratic-equations
roots
descriptive
0
votes
0
answers
19
ISI2017-MMA-3
If $\alpha, \beta$ and $\gamma$ are the roots of the equation $x^3+3x^2-8x+1=0$, then an equation whose roots are $\alpha+1, \beta+1$ and $\gamma+1$ is given by $y^3-11y+11=0$ $y^3-11y-11=0$ $y^3+13y+13=0$ $y^3+6y^2+y-3=0$
go_editor
asked
in
Quantitative Aptitude
Sep 15, 2018
by
go_editor
470
views
isi2017-mmamma
quantitative-aptitude
cubic-equations
roots
1
vote
2
answers
20
ISI2016-MMA-3
The number of real roots of the equation $2 \cos \big(\frac{x^2+x}{6}\big)=2^x+2^{-x}$ is $0$ $1$ $2$ $\infty$
go_editor
asked
in
Quantitative Aptitude
Sep 13, 2018
by
go_editor
503
views
isi2016-mmamma
trigonometry
quadratic-equations
roots
0
votes
0
answers
21
ISI2016-MMA-29
Suppose $a$ is a real number for which all the roots of the equation $x^4 -2ax^2+x+a^2-a=0$ are real. Then $a<-\frac{2}{3}$ $a=0$ $0<a<\frac{3}{4}$ $a \geq \frac{3}{4}$
go_editor
asked
in
Quantitative Aptitude
Sep 13, 2018
by
go_editor
220
views
isi2016-mmamma
quantitative-aptitude
quadratic-equations
roots
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