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Recent questions tagged quadratic-equations
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1
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1
ISI2014-DCG-11
Let $x_1$ and $x_2$ be the roots of the quadratic equation $x^2-3x+a=0$, and $x_3$ and $x_4$ be the roots of the quadratic equation $x^2-12x+b=0$. 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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isi2014-dcg
quadratic-equations
roots
geometric-progression
+1
vote
2
answers
2
ISI2014-DCG-22
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
in
Numerical Ability
by
Arjun
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424k
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27
views
isi2014-dcg
numerical-ability
quadratic-equations
+1
vote
1
answer
3
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
asked
Sep 23
in
Numerical Ability
by
Arjun
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424k
points)
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20
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isi2014-dcg
numerical-ability
quadratic-equations
roots
0
votes
0
answers
4
ISI2014-DCG-48
If $x$ is real, the set of real values of $a$ for which the function $y=x^2-ax+1-2a^2$ 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
in
Calculus
by
Arjun
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424k
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7
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isi2014-dcg
calculus
functions
quadratic-equations
0
votes
1
answer
5
ISI2014-DCG-55
If $a,b,c$ are sides of a triangle $ABC$ such that $x^2-2(a+b+c)x+3 \lambda (ab+bc+ca)=0$ 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
in
Numerical Ability
by
Arjun
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(
424k
points)
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18
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isi2014-dcg
numerical-ability
geometry
quadratic-equations
0
votes
1
answer
6
ISI2015-MMA-13
The number of real roots of the equation $2 \cos \bigg( \frac{x^2+x}{6} \bigg) = 2^x +2^{-x} \text{ is }$ $0$ $1$ $2$ infinitely many
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
424k
points)
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12
views
isi2015-mma
numerical-ability
quadratic-equations
trigonometry
0
votes
1
answer
7
ISI2015-MMA-15
The number of real solutions of the equations $(9/10)^x = -3+x-x^2$ is $2$ $0$ $1$ none of the above
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
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424k
points)
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15
views
isi2015-mma
numerical-ability
number-system
quadratic-equations
non-gate
+1
vote
2
answers
8
ISI2015-MMA-16
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
in
Numerical Ability
by
Arjun
Veteran
(
424k
points)
|
42
views
isi2015-mma
numerical-ability
quadratic-equations
functions
non-gate
0
votes
1
answer
9
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 $2$ $4$ $3$ $1$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)
|
33
views
isi2015-dcg
numerical-ability
quadratic-equations
roots
+1
vote
1
answer
10
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
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)
|
14
views
isi2015-dcg
numerical-ability
quadratic-equations
roots
0
votes
1
answer
11
ISI2015-DCG-26
If $r$ be the ratio of the roots of the equation $ax^{2}+bx+c=0,$ then $\frac{r}{b}=\frac{r+1}{ac}$ $\frac{r+1}{b}=\frac{r}{ac}$ $\frac{(r+1)^{2}}{r}=\frac{b^{2}}{ac}$ $\left(\frac{r}{b}\right)^{2}=\frac{r+1}{ac}$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)
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10
views
isi2015-dcg
numerical-ability
quadratic-equations
roots
0
votes
1
answer
12
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 $(ac)^{\frac{n}{n+1}} +b=0$ $(ac)^{\frac{n+1}{n}} +b=0$ $(ac^{n})^{\frac{1}{n+1}} +(a^nc)^{\frac{1}{n+1}}+b=0$ $(ac^{\frac{1}{n+1}})^n +(a^{\frac{1}{n+1}}c)^{n+1}+b=0$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)
|
13
views
isi2015-dcg
numerical-ability
quadratic-equations
roots
+2
votes
1
answer
13
ISI2015-DCG-29
The condition that ensures that the roots of the equation $x^3-px^2+qx-r=0$ are in $H.P.$ is $r^2-9pqr+q^3=0$ $27r^2-9pqr+3q^3=0$ $3r^3-27pqr-9q^3=0$ $27r^2-9pqr+2q^3=0$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)
|
24
views
isi2015-dcg
numerical-ability
quadratic-equations
cubic-equation
0
votes
1
answer
14
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
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)
|
15
views
isi2015-dcg
numerical-ability
quadratic-equations
roots
0
votes
1
answer
15
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 $2$ $4$ $3$ $1$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)
|
13
views
isi2016-dcg
numerical-ability
quadratic-equations
roots
+1
vote
1
answer
16
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
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)
|
15
views
isi2016-dcg
numerical-ability
quadratic-equations
roots
+1
vote
2
answers
17
ISI2016-DCG-26
If $r$ be the ratio of the roots of the equation $ax^{2}+bx+c=0,$ then $\frac{r}{b}=\frac{r+1}{ac}$ $\frac{r+1}{b}=\frac{r}{ac}$ $\frac{(r+1)^{2}}{r}=\frac{b^{2}}{ac}$ $\left(\frac{r}{b}\right)^{2}=\frac{r+1}{ac}$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)
|
30
views
isi2016-dcg
numerical-ability
quadratic-equations
roots
+1
vote
1
answer
18
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 $(ac)^{\frac{n}{n+1}}+b=0$ $(ac)^{\frac{n+1}{n}}+b=0$ $(ac^{n})^{\frac{1}{n+1}}+(a^{n}c)^{\frac{1}{n+1}}+b=0$ $(ac^\frac{1}{n+1})^{n}+(a^\frac{1}{n+1}c)^{n+1}+b=0$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)
|
14
views
isi2016-dcg
numerical-ability
quadratic-equations
roots
+1
vote
0
answers
19
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 $r^{2}-9pqr+q^{3}=0$ $27r^{2}-9pqr+3q^{3}=0$ $3r^{3}-27pqr-9q^{3}=0$ $27r^{2}-9pqr+2q^{3}=0$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)
|
9
views
isi2016-dcg
numerical-ability
quadratic-equations
roots
0
votes
1
answer
20
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.
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)
|
17
views
isi2016-dcg
numerical-ability
quadratic-equations
roots
0
votes
1
answer
21
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 $0$ $1$ $2$ $5$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)
|
19
views
isi2017-dcg
numerical-ability
quadratic-equations
roots
+1
vote
1
answer
22
ISI2016-PCB-A-1
If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+6x+1=0$, then prove that $\frac{\alpha}{\beta} + \frac{\beta}{\alpha} + \frac{\beta}{\gamma}+ \frac{\gamma}{\beta} + \frac{\gamma}{\alpha}+ \frac{\alpha}{\gamma}=-3.$
asked
Sep 18, 2018
in
Numerical Ability
by
jothee
Veteran
(
105k
points)
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34
views
isi2016-pcb-a
numerical-ability
quadratic-equations
roots
descriptive
+1
vote
1
answer
23
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 $0$ $1$ $2$ $\infty$
asked
Sep 13, 2018
in
Numerical Ability
by
jothee
Veteran
(
105k
points)
|
22
views
isi2016-mmamma
trigonometry
quadratic-equations
roots
0
votes
0
answers
24
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 $a<-\frac{2}{3}$ $a=0$ $0<a<\frac{3}{4}$ $a \geq \frac{3}{4}$
asked
Sep 13, 2018
in
Numerical Ability
by
jothee
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(
105k
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10
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isi2016-mmamma
numerical-ability
quadratic-equations
roots
+2
votes
2
answers
25
GATE2018 EE: GA-4
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
(
54.8k
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312
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gate2018-ee
general-aptitude
numerical-ability
easy
quadratic-equations
0
votes
1
answer
26
GATE2018 ME-1: GA-7
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
(
424k
points)
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62
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gate2018-me-1
general-aptitude
numerical-ability
quadratic-equations
system-of-equations
+3
votes
1
answer
27
ISI 2015 PCB A2
Find all real solutions of the equation $x^{2} - |x-1| - 3 = 0$
asked
Mar 4, 2017
in
Others
by
Devasish Ghosh
Junior
(
815
points)
|
217
views
engineering-mathematics
quadratic-equations
isi2015
+2
votes
1
answer
28
GATE2016 EC-2: GA-4
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
(
30.1k
points)
|
299
views
gate2016-ec-2
numerical-ability
quadratic-equations
+8
votes
1
answer
29
Radix+Quadratic equation
asked
Oct 12, 2016
in
Digital Logic
by
Rahul Jain25
Boss
(
11.1k
points)
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731
views
digital-logic
quadratic-equations
radix
number-representation
+1
vote
1
answer
30
UGCNET-June2013-III-11
The golden ratio $\varphi$ and its conjugate $\bar{\varphi}$ both satisfy the equation $x^3 –x-1=0$ $x^3 +x-1=0$ $x^2 –x-1=0$ $x^2 +x-1=0$
asked
Jul 16, 2016
in
Others
by
jothee
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105k
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372
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ugcnetjune2013iii
quadratic-equations
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