Question

If a root of the equations x^2+px+q=0 and x^2+alphax+beta =0 is common, then its value will be (where p not equal a and q not equal to beta)
please answer asap

Answer 1

ANSWER

f α & β are the roots of

$$px2+qx+r=0$$

then

$$αβ=−qp$$

αβ=rp

_______________________________

x2+ax+b=0−−−(1)

x2+cx+d=0−−−(2)

let the common root be α

for eqn(1)

α+α=−a

⇒α=−a2

& α2=b

for the eqn(2) let the second root be β

then

α+β=−c

αβ=d

⇒β=dα

∴α+dα=−c

α2+d=α(−c)

b+d=(−a2)(−c)

∴2(b+d)=ac as reqd.