Question

If one root of the equation $x^2-4x+k=0$ is $2-i$, find the other root and the value of k.

Answer 1

Other root: 2+i, k=5

Answer 2

If coefficients are real, complex roots appear in conjugate pairs. One root $2-i$, so other root is $2+i$.

Sum of roots $=(2-i)+(2+i)=4$. From equation, sum $= -(-4)/1 = 4$.

Product of roots $=(2-i)(2+i)=5$. From equation, product $= k/1 = k$. Thus $k=5$.