Question

if the quadratic equation ax^2+bx+c =0(a,b,c€real) and x^2+4x+5=0 have a common root, then a,b,c must satisfy the relation​

Answer 1

Explanation:

for this problem we will use the property of the sum and product of roots of a quadratic

that is

if  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