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

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

Question

(B) Let $\alpha$ be the common root of the two equations.Then,$\alpha^2 + p\alpha + 2q = 0$ and $\alpha^2 + q\alpha + 2p = 0$.Subtracting the second e

Vedclass · Accepted Answer

$-2$

Vedclass · Answer

(B) Let $\alpha$ be the common root of the two equations.Then,$\alpha^2 + p\alpha + 2q = 0$ and $\alpha^2 + q\alpha + 2p = 0$.Subtracting the second equation from the first,we get:$(\alpha^2 + p\alpha + 2q) - (\alpha^2 + q\alpha + 2p) = 0$$\alpha(p - q) - 2(p - q) = 0$$(p - q)(\alpha - 2) = 0$Since it is given that $p 
e q$,we must have $\alpha - 2 = 0$,which implies $\alpha = 2$.Substituting $\alpha = 2$ into the first equation:$(2)^2 + p(2) + 2q = 0$$4 + 2p + 2q = 0$$2(p + q) = -4$$p + q = -2$

If the equations $x^2 + px + 2q = 0$ and $x^2 + qx + 2p = 0$ $(p \ne q)$ have a common root,then the value of $p + q$ is

Similar Questions

If the ratio of the roots of the equation $ax^2 + bx + c = 0$ is $p:q$,then:

If the roots of the given equation $({m^2} + 1){x^2} + 2amx + {a^2} - {b^2} = 0$ are equal,then

Find the number of natural number solutions for the equation $x_1 + x_2 = 100$,such that $x_1$ and $x_2$ are not multiples of $5$.

If $3p^2 = 5p + 2$ and $3q^2 = 5q + 2$ where $p \ne q$,then the equation whose roots are $3p - 2q$ and $3q - 2p$ is

Solve the given two equations and provide the correct answer from the given options.
$I.$ $391 x^{2} + 1344 x + 1073 = 0$
$II.$ $437 y^{2} + 1074 y + 589 = 0$

Vedclass Test Series

Exam Paper Generator

Online Exam Module