Question

The equations x
2 − 4x + k = 0 and x
2 + kx − 4 = 0, where k is a real number, have exactly
one common root. What is the value of k?

Answer 1

hey mate

Let the common root be alpha

$2 - 4( \alpha ) + k \: = 2 + k( \alpha ) - 4 = 0$
2 + k - 4(alpha) = 2 -4 +k(alpha)
2 - 2 + k + 4 = k ( alpha ) + 4 ( alpha )
k + 4 = alpha ( k + 4 )
alpha = k + 4 / k + 4
alpha = 1

we know that alpha is 1 so when we substitute in the equation

2 - 4(1) + k = 2 + k(1) - 4
2 - 2 - 4 +4 + k - k = 0

from this we got to know that the equation obtained is 0

and so k = 0

hope it helps pls make as brainliest