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Recent questions tagged roots
+1
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1
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1
ISI2014DCG11
Let $x_1$ and $x_2$ be the roots of the quadratic equation $x^23x+a=0$, and $x_3$ and $x_4$ be the roots of the quadratic equation $x^212x+b=0$. If $x_1, x_2, x_3$ and $x_4 \: (0 < x_1 < x_2 < x_3 < x_4)$ are in $G.P.,$ then $ab$ equals $64$ $5184$ $64$ $5184$
asked
Sep 23
in
Numerical Ability
by
Arjun
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425k
points)

27
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isi2014dcg
quadraticequations
roots
geometricprogression
+1
vote
1
answer
2
ISI2014DCG30
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
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

22
views
isi2014dcg
numericalability
quadraticequations
roots
0
votes
0
answers
3
ISI2014DCG54
The number of real roots of the equation $1+\cos ^2x+\cos ^3 x – \cos^4x=5$ is equal to $0$ $1$ $3$ $4$
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

26
views
isi2014dcg
numericalability
trigonometry
roots
0
votes
1
answer
4
ISI2015MMA12
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 $(32i)$ are two two roots of this polynomial then the value of $a$ is $524/65$ $524/65$ $1/65$ $1/65$
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

18
views
isi2015mma
numericalability
numbersystem
polynomial
roots
nongate
0
votes
1
answer
5
ISI2015DCG7
Let $x^22(4k1)x+15k^22k7>0$ for any real value of $x$. Then the integer value of $k$ is $2$ $4$ $3$ $1$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

33
views
isi2015dcg
numericalability
quadraticequations
roots
+1
vote
1
answer
6
ISI2015DCG25
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 $x^2+2x+63=0$ $x^263x+2=0$ $x^22x63=0$ None of the above
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

14
views
isi2015dcg
numericalability
quadraticequations
roots
0
votes
1
answer
7
ISI2015DCG26
If $r$ be the ratio of the roots of the equation $ax^{2}+bx+c=0,$ then $\frac{r}{b}=\frac{r+1}{ac}$ $\frac{r+1}{b}=\frac{r}{ac}$ $\frac{(r+1)^{2}}{r}=\frac{b^{2}}{ac}$ $\left(\frac{r}{b}\right)^{2}=\frac{r+1}{ac}$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

10
views
isi2015dcg
numericalability
quadraticequations
roots
0
votes
1
answer
8
ISI2015DCG28
If one root of a quadratic equation $ax^2+bx+c=0$ be equal to the $n^{th}$ power of the other, then $(ac)^{\frac{n}{n+1}} +b=0$ $(ac)^{\frac{n+1}{n}} +b=0$ $(ac^{n})^{\frac{1}{n+1}} +(a^nc)^{\frac{1}{n+1}}+b=0$ $(ac^{\frac{1}{n+1}})^n +(a^{\frac{1}{n+1}}c)^{n+1}+b=0$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

13
views
isi2015dcg
numericalability
quadraticequations
roots
0
votes
1
answer
9
ISI2015DCG30
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
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

15
views
isi2015dcg
numericalability
quadraticequations
roots
0
votes
1
answer
10
ISI2016DCG7
Let $x^{2}2(4k1)x+15k^{2}2k7>0$ for any real value of $x$. Then the integer value of $k$ is $2$ $4$ $3$ $1$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

13
views
isi2016dcg
numericalability
quadraticequations
roots
+1
vote
1
answer
11
ISI2016DCG25
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 $x^{2}+2x+63=0$ $x^{2}63x+2=0$ $x^{2}2x63=0$ None of these
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

15
views
isi2016dcg
numericalability
quadraticequations
roots
+1
vote
2
answers
12
ISI2016DCG26
If $r$ be the ratio of the roots of the equation $ax^{2}+bx+c=0,$ then $\frac{r}{b}=\frac{r+1}{ac}$ $\frac{r+1}{b}=\frac{r}{ac}$ $\frac{(r+1)^{2}}{r}=\frac{b^{2}}{ac}$ $\left(\frac{r}{b}\right)^{2}=\frac{r+1}{ac}$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

30
views
isi2016dcg
numericalability
quadraticequations
roots
+1
vote
1
answer
13
ISI2016DCG28
If one root of a quadratic equation $ax^{2}+bx+c=0$ be equal to the n th power of the other, then $(ac)^{\frac{n}{n+1}}+b=0$ $(ac)^{\frac{n+1}{n}}+b=0$ $(ac^{n})^{\frac{1}{n+1}}+(a^{n}c)^{\frac{1}{n+1}}+b=0$ $(ac^\frac{1}{n+1})^{n}+(a^\frac{1}{n+1}c)^{n+1}+b=0$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

14
views
isi2016dcg
numericalability
quadraticequations
roots
+1
vote
0
answers
14
ISI2016DCG29
The condition that ensures that the roots of the equation $x^{3}px^{2}+qxr=0$ are in H.P. is $r^{2}9pqr+q^{3}=0$ $27r^{2}9pqr+3q^{3}=0$ $3r^{3}27pqr9q^{3}=0$ $27r^{2}9pqr+2q^{3}=0$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

9
views
isi2016dcg
numericalability
quadraticequations
roots
0
votes
1
answer
15
ISI2016DCG30
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.
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

17
views
isi2016dcg
numericalability
quadraticequations
roots
0
votes
1
answer
16
ISI2017DCG5
The sum of the squares of the roots of $x^2(a2)xa1=0$ becomes minimum when $a$ is $0$ $1$ $2$ $5$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

20
views
isi2017dcg
numericalability
quadraticequations
roots
+1
vote
0
answers
17
ISI2018DCG11
The sum of $99^{th}$ power of all the roots of $x^71=0$ is equal to $1$ $2$ $1$ $0$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

18
views
isi2018dcg
numericalability
polynomials
roots
0
votes
1
answer
18
ISI2017PCBA1
Suppose all the roots of the equation $x^3 +bx2017=0$ (where $b$ is a real number) are real. Prove that exactly one root is positive.
asked
Sep 19, 2018
in
Numerical Ability
by
jothee
Veteran
(
105k
points)

44
views
isi2017pcba
numericalability
cubicequations
roots
descriptive
+1
vote
1
answer
19
ISI2016PCBA1
If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+6x+1=0$, then prove that $\frac{\alpha}{\beta} + \frac{\beta}{\alpha} + \frac{\beta}{\gamma}+ \frac{\gamma}{\beta} + \frac{\gamma}{\alpha}+ \frac{\alpha}{\gamma}=3.$
asked
Sep 18, 2018
in
Numerical Ability
by
jothee
Veteran
(
105k
points)

34
views
isi2016pcba
numericalability
quadraticequations
roots
descriptive
0
votes
0
answers
20
ISI2017MMA3
If $\alpha, \beta$ and $\gamma$ are the roots of the equation $x^3+3x^28x+1=0$, then an equation whose roots are $\alpha+1, \beta+1$ and $\gamma+1$ is given by $y^311y+11=0$ $y^311y11=0$ $y^3+13y+13=0$ $y^3+6y^2+y3=0$
asked
Sep 15, 2018
in
Numerical Ability
by
jothee
Veteran
(
105k
points)

36
views
isi2017mmamma
numericalability
cubicequations
roots
+1
vote
1
answer
21
ISI2016MMA3
The number of real roots of the equation $2 \cos \big(\frac{x^2+x}{6}\big)=2^x+2^{x}$ is $0$ $1$ $2$ $\infty$
asked
Sep 13, 2018
in
Numerical Ability
by
jothee
Veteran
(
105k
points)

22
views
isi2016mmamma
trigonometry
quadraticequations
roots
0
votes
0
answers
22
ISI2016MMA29
Suppose $a$ is a real number for which all the roots of the equation $x^4 2ax^2+x+a^2a=0$ are real. Then $a<\frac{2}{3}$ $a=0$ $0<a<\frac{3}{4}$ $a \geq \frac{3}{4}$
asked
Sep 13, 2018
in
Numerical Ability
by
jothee
Veteran
(
105k
points)

10
views
isi2016mmamma
numericalability
quadraticequations
roots
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