If a root of the equations x^2+px+q=0 and x^2 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the common root be $y$. Then $y^2+py+q=0$ and $y^2+\alpha y+\beta=0$. Subtracting the two equations: $(y^2+py+q) - (y^2+\alpha y+\beta) = 0$ $

Vedclass · Accepted Answer

$\frac{q-\beta}{\alpha-p}$ or $\frac{p\beta-\alpha q}{q-\beta}$

Vedclass · Answer

(C) Let the common root be $y$. Then $y^2+py+q=0$ and $y^2+\alpha y+\beta=0$. Subtracting the two equations: $(y^2+py+q) - (y^2+\alpha y+\beta) = 0$ $(p-\alpha)y + (q-\beta) = 0$ $y = \frac{\beta-q}{p-\alpha} = \frac{q-\beta}{\alpha-p}$. Alternatively,using the cross-multiplication method for the system: $\frac{y^2}{p\beta-q\alpha} = \frac{y}{q-\beta} = \frac{1}{\alpha-p}$. From the second and third parts,$y = \frac{q-\beta}{\alpha-p}$. From the first and second parts,$y = \frac{p\beta-q\alpha}{q-\beta}$. Since both expressions represent the same common root $y$,the value is $\frac{q-\beta}{\alpha-p}$ or $\frac{p\beta-q\alpha}{q-\beta}$.

If a root of the equations $x^2+px+q=0$ and $x^2+\alpha x+\beta=0$ is common,then its value will be (where $p \neq \alpha$ and $q \neq \beta$)

Similar Questions

$A$ mass $m$ moves with a velocity $v$ and collides inelastically with another identical mass initially at rest. After collision,the first mass moves with velocity $\frac{v}{\sqrt{3}}$ in a direction perpendicular to its initial direction of motion. The speed of the second mass after collision is:

Which of the following reactions will not result in the formation of carbon-carbon bonds?

$e^{\log (\cosh^{-1} 2)}$ is equal to :

If a point $(x, y) = (\tan \theta + \sin \theta, \tan \theta - \sin \theta)$,then the locus of $(x, y)$ is

If $\Delta U$ and $\Delta W$ represent the increase in internal energy and work done by the system respectively in a thermodynamic process,which of the following is true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module