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Q.
If $1 - i$ , is a root of the equation $x^{2} + ax + b = 0$, where $a, b \in R$, then find the values of $a$ and $b$.
Complex Numbers and Quadratic Equations
Solution:
Since complex roots always occur in conjugate pair.
$\therefore $ Other conjugate root is $1+i$.
Sum of roots $=\frac{-a}{1}=\left(1-i\right)+\left(1+i\right)$
$\Rightarrow a=-2$.
Products of roots $=\frac{b}{1}=\left(1-i\right)\left(1+i\right)$
$\Rightarrow b=2$