Question

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 $b$.

• A. $a=-2$ and $b=5$
• B. $a=-2$ and $b=2$
• C. $a=2$ and $b=2$
• D. None of these

Answer 1

Answer: (B)

$a=-2$ and $b=2$

$\therefore (1-i)$ is a root of $x^2+ax+b=0$

$\therefore$ Other root is $(1+i)$

$\therefore (x-1+i)(x-1-i)=0$

$\Rightarrow x^2+(-1+i-1-i)x+(i-1)(-i-1)=0$

$\Rightarrow x^2-2x+2=0$

$\therefore a=-2,b=2$