Question

The equations x^2+2x+k=0and x^2+4x-k=0 have a common root alpha then find the value of k

Answer 1

$\alpha$
is nothing but a variable
on putting
$\alpha$
in x^2+2x+k=0
$\alpha ^{2} + 2 \alpha + k = 0$
on putting
$\alpha$
in x^2+4x-k=0
$\alpha ^{2} + 4 \alpha - k = 0$
$as \: \alpha \: is \: common \: root \: of \: both \: the \: equations \: then \: eq.1 = eq.2$

$\alpha {2} + 2 \alpha + k = \alpha ^{2} + 4 \alpha - k$
Therefore
2k = 2alpha
k= alpha