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Recent questions tagged quadratic-equations

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Best Open Video Playlist for Quadratic Equations Topic | Quantitative Aptitude
Please list out the best free available video playlist for Quadratic Equations from Quantitative Aptitude as an answer here (only one playlist per answer). We'll then select the best playlist and add to GO classroom ... ones are more likely to be selected as best. For the full list of selected videos please see here

makhdoom ghaya asked in Study Resources Aug 28

by makhdoom ghaya

29 views

4 votes

1 answer

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GATE CSE 2022 | GA Question: 3
Let $r$ be a root of the equation $x^{2} + 2x + 6 = 0.$ Then the value of the expression $(r+2) (r+3) (r+4) (r+5)$ is $51$ $-51$ $126$ $-126$

Arjun asked in Quantitative Aptitude Feb 15

by Arjun

1.4k views

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1 answer

3

Given that the r is the root of the quadratic equation $x^2 + 2x + 6=0.$
Given that $r$ is the root of the quadratic equation $x^2 + 2x + 6=0,$ what is the value of the expression $(r+2)(r+3)(r+4)(r+5)?$

umangbhatt asked in Quantitative Aptitude Feb 6

365 views

8 votes

3 answers

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GATE CSE 2021 Set 2 | GA Question: 4
If $\left( x – \dfrac{1}{2} \right)^2 – \left( x- \dfrac{3}{2} \right) ^2 = x+2$, then the value of $x$ is: $2$ $4$ $6$ $8$

Arjun asked in Quantitative Aptitude Feb 18, 2021

by Arjun

1.9k views

1 vote

2 answers

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UGC NET CSE | October 2020 | Part 2 | Question: 8
What is the radix of the numbers if the solution to the quadratic equation $x^2-10x+26=0$ is $x=4$ and $x=7$? $8$ $9$ $10$ $11$

go_editor asked in Quantitative Aptitude Nov 20, 2020

1.6k views

3 votes

2 answers

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GATE ECE 2020 | GA Question: 9
$a, b, c$ are real numbers. The quadratic equation $ax^{2}-bx+c=0$ has equal roots, which is $\beta$, then $\beta =b/a$ $\beta^{2} =ac$ $\beta^{3} =bc/\left ( 2a^{2} \right )$ $\beta^{2} \neq 4ac$

go_editor asked in Quantitative Aptitude Feb 13, 2020

562 views

1 vote

1 answer

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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 $64$ $5184$ $-64$ $-5184$

Arjun asked in Quantitative Aptitude Sep 23, 2019

by Arjun

294 views

2 votes

2 answers

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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.

Arjun asked in Quantitative Aptitude Sep 23, 2019

by Arjun

316 views

2 votes

1 answer

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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

267 views

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1 answer

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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

Arjun asked in Calculus Sep 23, 2019

by Arjun

193 views

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1 answer

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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 $\lambda < \frac{4}{3}$ $\lambda > \frac{5}{3}$ $\lambda \in \big( \frac{4}{3}, \frac{5}{3}\big)$ $\lambda \in \big( \frac{1}{3}, \frac{5}{3}\big)$

Arjun asked in Quantitative Aptitude Sep 23, 2019

by Arjun

236 views

1 vote

2 answers

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ISI2015-MMA-13
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

Arjun asked in Quantitative Aptitude Sep 23, 2019

by Arjun

527 views

1 vote

1 answer

13

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

Arjun asked in Quantitative Aptitude Sep 23, 2019

by Arjun

459 views

2 votes

3 answers

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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

Arjun asked in Quantitative Aptitude Sep 23, 2019

by Arjun

509 views

0 votes

1 answer

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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

257 views

1 vote

1 answer

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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

238 views

0 votes

1 answer

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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

158 views

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1 answer

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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

138 views

0 votes

1 answer

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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

160 views

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1 answer

20

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

154 views

1 vote

1 answer

21

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

176 views

1 vote

2 answers

22

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

245 views

1 vote

1 answer

23

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

256 views

1 vote

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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

155 views

0 votes

1 answer

25

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

183 views

0 votes

1 answer

26

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

218 views

2 votes

3 answers

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NIELIT 2018-17
If $2a+3b+c=0$, then at least one root of the equation $ax^2+bx+c=0$, lies in the interval: $(0,1)$ $(1,2)$ $(2,3)$ $(1,3)$

Arjun asked in Quantitative Aptitude Dec 7, 2018

by Arjun

497 views

1 vote

1 answer

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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

286 views

1 vote

2 answers

29

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

322 views

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Recent questions tagged quadratic-equations