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Recent questions tagged quadraticequations
+1
vote
1
answer
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, 2019
in
Numerical Ability
by
Arjun
Veteran
(
430k
points)

54
views
isi2014dcg
quadraticequations
+1
vote
2
answers
2
ISI2014DCG22
The conditions on $a$, $b$ and $c$ under which the roots of the quadratic equation $ax^2+bx+c=0 \: ,a \neq 0, \: b \neq 0 $ and $c \neq 0$, are unequal magnitude but of the opposite signs, are the following: $a$ and $c$ have the same sign while $b$ has the ... $c$ has the opposite sign. $a$ and $c$ have the same sign. $a$, $b$ and $c$ have the same sign.
asked
Sep 23, 2019
in
Numerical Ability
by
Arjun
Veteran
(
430k
points)

45
views
isi2014dcg
numericalability
quadraticequations
+1
vote
1
answer
3
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, 2019
in
Numerical Ability
by
Arjun
Veteran
(
430k
points)

35
views
isi2014dcg
numericalability
quadraticequations
roots
0
votes
0
answers
4
ISI2014DCG48
If $x$ is real, the set of real values of $a$ for which the function $y=x^2ax+12a^2$ is always greater than zero is $ \frac{2}{3} < a \leq \frac{2}{3}$ $ \frac{2}{3} \leq a < \frac{2}{3}$ $ \frac{2}{3} < a < \frac{2}{3}$ None of these
asked
Sep 23, 2019
in
Calculus
by
Arjun
Veteran
(
430k
points)

12
views
isi2014dcg
calculus
functions
quadraticequations
0
votes
1
answer
5
ISI2014DCG55
If $a,b,c$ are sides of a triangle $ABC$ such that $x^22(a+b+c)x+3 \lambda (ab+bc+ca)=0$ has real roots then $\lambda < \frac{4}{3}$ $\lambda > \frac{5}{3}$ $\lambda \in \big( \frac{4}{3}, \frac{5}{3}\big)$ $\lambda \in \big( \frac{1}{3}, \frac{5}{3}\big)$
asked
Sep 23, 2019
in
Numerical Ability
by
Arjun
Veteran
(
430k
points)

31
views
isi2014dcg
numericalability
geometry
quadraticequations
0
votes
1
answer
6
ISI2015MMA13
The number of real roots of the equation $2 \cos \left( \frac{x^2+x}{6} \right) = 2^x +2^{x} \text{ is }$ $0$ $1$ $2$ infinitely many
asked
Sep 23, 2019
in
Numerical Ability
by
Arjun
Veteran
(
430k
points)

16
views
isi2015mma
numericalability
quadraticequations
trigonometry
0
votes
1
answer
7
ISI2015MMA15
The number of real solutions of the equations $(9/10)^x = 3+xx^2$ is $2$ $0$ $1$ none of the above
asked
Sep 23, 2019
in
Numerical Ability
by
Arjun
Veteran
(
430k
points)

20
views
isi2015mma
numericalability
numbersystem
quadraticequations
nongate
+1
vote
2
answers
8
ISI2015MMA16
If two real polynomials $f(x)$ and $g(x)$ of degrees $m\: (\geq 2)$ and $n\: (\geq 1)$ respectively, satisfy $f(x^2+1)=f(x)g(x),$ for every $x \in \mathbb{R}$, then $f$ has exactly one real root $x_0$ such that $f’(x_0) \neq 0$ $f$ has exactly one real root $x_0$ such that $f’(x_0) = 0$ $f$ has $m$ distinct real roots $f$ has no real root
asked
Sep 23, 2019
in
Numerical Ability
by
Arjun
Veteran
(
430k
points)

51
views
isi2015mma
numericalability
quadraticequations
functions
nongate
0
votes
1
answer
9
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, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.4k
points)

36
views
isi2015dcg
numericalability
quadraticequations
roots
+1
vote
1
answer
10
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, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.4k
points)

20
views
isi2015dcg
numericalability
quadraticequations
roots
0
votes
1
answer
11
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, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.4k
points)

12
views
isi2015dcg
numericalability
quadraticequations
roots
0
votes
1
answer
12
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, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.4k
points)

17
views
isi2015dcg
numericalability
quadraticequations
roots
0
votes
1
answer
13
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, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.4k
points)

17
views
isi2015dcg
numericalability
quadraticequations
roots
0
votes
1
answer
14
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, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.4k
points)

21
views
isi2016dcg
numericalability
quadraticequations
roots
+1
vote
1
answer
15
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, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.4k
points)

21
views
isi2016dcg
numericalability
quadraticequations
roots
+1
vote
2
answers
16
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, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.4k
points)

34
views
isi2016dcg
numericalability
quadraticequations
roots
+1
vote
1
answer
17
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, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.4k
points)

26
views
isi2016dcg
numericalability
quadraticequations
roots
+1
vote
0
answers
18
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, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.4k
points)

14
views
isi2016dcg
numericalability
quadraticequations
roots
0
votes
1
answer
19
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, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.4k
points)

23
views
isi2016dcg
numericalability
quadraticequations
roots
0
votes
1
answer
20
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, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.4k
points)

25
views
isi2017dcg
numericalability
quadraticequations
roots
+1
vote
1
answer
21
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)

37
views
isi2016pcba
numericalability
quadraticequations
roots
descriptive
+1
vote
1
answer
22
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)

28
views
isi2016mmamma
trigonometry
quadraticequations
roots
0
votes
0
answers
23
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)

15
views
isi2016mmamma
numericalability
quadraticequations
roots
+2
votes
2
answers
24
GATE2018 EE: GA4
For what values of $k$ given below is $\dfrac{(k + 2)^2}{(k  3)}$ an integer? $4, 8, 18$ $4, 10, 16$ $4, 8, 28$ $8, 26, 28$
asked
Feb 21, 2018
in
Numerical Ability
by
Lakshman Patel RJIT
Veteran
(
58.5k
points)

335
views
gate2018ee
generalaptitude
numericalability
easy
quadraticequations
0
votes
1
answer
25
GATE2018 ME1: GA7
Given that $a$ and $b$ are integers and $a+a^2 b^3$ is odd, which of the following statements is correct? $a$ and $b$ are both odd $a$ and $b$ are both even $a$ is even and $b$ is odd $a$ is odd and $b$ is even
asked
Feb 17, 2018
in
Numerical Ability
by
Arjun
Veteran
(
430k
points)

91
views
gate2018me1
generalaptitude
numericalability
quadraticequations
systemofequations
+3
votes
1
answer
26
ISI 2015 PCB A2
Find all real solutions of the equation $x^{2}  x1  3 = 0$
asked
Mar 4, 2017
in
Others
by
Devasish Ghosh
Junior
(
845
points)

224
views
engineeringmathematics
quadraticequations
isi2015
+4
votes
1
answer
27
GATE2016 EC2: GA4
Given $(9 \text{ inches}) ^{\frac{1}{2}} = (0.25\text{ yards}) ^{\frac{1}{2}},$ which one of the following statements is TRUE? $3$ inches = $0.5$ yards $9$ inches = $1.5$ yards $9$ inches = $0.25$ yards $81$ inches = $0.0625$ yards
asked
Jan 21, 2017
in
Numerical Ability
by
makhdoom ghaya
Boss
(
30.6k
points)

357
views
gate2016ec2
numericalability
quadraticequations
+8
votes
1
answer
28
Radix+Quadratic equation
asked
Oct 12, 2016
in
Digital Logic
by
Rahul Jain25
Boss
(
11.1k
points)

751
views
digitallogic
quadraticequations
radix
numberrepresentation
+1
vote
1
answer
29
UGCNETJune2013III11
The golden ratio $\varphi$ and its conjugate $\bar{\varphi}$ both satisfy the equation $x^3 –x1=0$ $x^3 +x1=0$ $x^2 –x1=0$ $x^2 +x1=0$
asked
Jul 16, 2016
in
Others
by
jothee
Veteran
(
105k
points)

381
views
ugcnetjune2013iii
quadraticequations
+1
vote
1
answer
30
B.Stat. 2005
If $\sqrt{3}$ + 1 is a root of equation 3 x$^{3}$ + ax$^{2}$ + bx + 12 = 0 where a and b are rational numbers, then b is equal to 6 2 6 10
asked
Mar 23, 2016
in
Numerical Ability
by
vijaycs
Boss
(
26.5k
points)

154
views
numericalability
quadraticequations
normal
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