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 equations $x^2 + px + 2q = 0$ and $x^2 + qx + 2p = 0$.Then,$\alpha^2 + p\alpha + 2q = 0$ and $\alpha^2 + q\

Vedclass · Accepted Answer

$-2$

Vedclass · Answer

(B) Let $\alpha$ be the common root of the equations $x^2 + px + 2q = 0$ and $x^2 + qx + 2p = 0$.Then,$\alpha^2 + p\alpha + 2q = 0$ and $\alpha^2 + q\alpha + 2p = 0$.Subtracting the two equations: $(\alpha^2 + p\alpha + 2q) - (\alpha^2 + q\alpha + 2p) = 0$.$\alpha(p - q) - 2(p - q) = 0$.$(p - q)(\alpha - 2) = 0$.Since $p 
eq q$,we must have $\alpha - 2 = 0$,which implies $\alpha = 2$.Substituting $\alpha = 2$ into the first equation: $(2)^2 + p(2) + 2q = 0$.$4 + 2p + 2q = 0$.$2(p + q) = -4$.Therefore,$p + q = -2$.

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

Similar Questions

If the equations $k(6x^2 + 3) + rx + 2x^2 - 1 = 0$ and $6k(2x^2 + 1) + px + 4x^2 - 2 = 0$ have common roots,then $2r - p = \dots$

If the equations $x^2 + px + q = 0$ and $x^2 + qx + p = 0$ have a common root,then $p + q + 1 = $

If a root of the equation $ax^2 + bx + c = 0$ is the reciprocal of a root of the equation $a'x^2 + b'x + c' = 0$,then:

If the equations $x^2+ax+b=0$ and $x^2+bx+a=0$ $(a \neq b)$ have a common root,then $a+b$ is equal to

The equations $x^2-ax+b=0$ and $x^2+bx-a=0$ have a common root. Then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module