Q. If the equation $x^{2}+px+2q=0$ and $x^{2}+qx+2p=0\left(\right.p\neq q\left.\right)$ have a common root
then the absolute value of $\left(\right.p+q\left.\right)$ is

NTA AbhyasNTA Abhyas 2022 Report Error

Solution:

We have,
$x^{2}+px+2q=0$
$x^{2}+qx+2p=0$
If $f\left(x\right)$ and $g\left(x\right)$ have common root then $f\left(x\right)\pmg\left(x\right)$ have same root common. Then,
$\left(x^{2} + p x + 2 q\right)-\left(x^{2} + q x + 2 p\right)=0$
$\Rightarrow x\left(\right.p-q\left.\right)-2\left(\right.p-q\left.\right)=0$
$\Rightarrow \left(x - 1\right)\left(p + q - 2\right)=0$
Hence, common root is
$p+q=-2$

Questions from NTA Abhyas 2022

1. The area bounded by $y=xe^{\left|x\right|}$ and the lines $\left|x\right|=1, \, y=0$ is

Application of Integrals

2. If $x=3$ is the chord of contact of the circle $x^{2}+y^{2}=81$ , then the equation of the corresponding pair of tangents is

Conic Sections

3. Let $z_{1}$ and $z_{2}$ be the $n^{t h}$ roots of unity which are ends of a line segment that subtend a right angle at the origin. Then, $n$ must be of the form

Complex Numbers and Quadratic Equations

4. In $\left(\right.0,2\pi \left.\right)$ , the total number of points, where $f\left(x\right)=max\left\{sin x , cos x , 1 - cos x\right\}$ is not differentiable, is

Continuity and Differentiability

5. Let $Ι_{1}=\displaystyle \int _{0}^{1} e^{x^{2}} d x$ and $Ι_{2}=\displaystyle \int _{0}^{1} 2 x^{2} e^{x^{2}} d x$ , then the value of $Ι_{1}+Ι_{2}$ is equal to

Mathematics Most Viewed Questions

1. The solution of $\frac{dy}{dx} = \frac{y}{x}+\tan \frac{y}{x}$ is

WBJEE 2011 Differential Equations

2. The solution of the differential equation $\frac{dy}{dx} = (x +y)^2$ is

COMEDK 2009 Differential Equations

3. If a and b are vectors such that $|a+b|=|a-b|$ then the angle between a and b is

KCET 2007 Vector Algebra

4. If $\begin{bmatrix}1&- \tan\theta \\ \tan \theta&1\end{bmatrix}\begin{bmatrix}1&\tan \theta \\ - \tan \theta &1\end{bmatrix}^{-1} = \begin{bmatrix}a&-b\\ b&a\end{bmatrix}$ then

COMEDK 2009 Matrices

5. $\int\frac{1}{\sin x\, \cos x}$ dx is equal to

KEAM 2016 Integrals

6. $\int\frac{\sin \frac{5x}{2}}{\sin \frac{x}{2}} dx $ is equal to :
(where $c$ is a constant of integration)

JEE Main 2019 Integrals

7. A particle is dropped under gravity from rest from a height $ h(g=9.8\,m/{{s}^{2}}) $ and it travels a distance $ \frac{9h}{25} $ in the last second the height $ h $ is:

Bihar CECE 2006

8. The value of $ \int{\frac{{{x}^{2}}+1}{{{x}^{4}}-{{x}^{2}}+1}}dx $ is

KEAM 2007 Integrals

9. The value of $\int \frac{x^2+1}{x^2-1}dx$ is

KCET 2007 Integrals

10. The value of the integral $\int\frac{cos x}{sin x + cos x}dx$ is equal to

KEAM 2013 Integrals

Q. If the equation $x^{2}+px+2q=0$ and $x^{2}+qx+2p=0\left(\right.p\neq q\left.\right)$ have a common root then the absolute value of $\left(\right.p+q\left.\right)$ is