If $1-i$ is a root of the equation $x^2+a x+b=0$ then $b$ is equal to

If $1-i$ is a root of the equation $x^2+a x+b=0$ then $b$ is equal to
  1. $1$
  2. $-1$
  3. $-2$
  4. $2$

Solution

Since $1-i$ is a ront of the equation $x^2+9 x+b=0$ then another root will be $1+i$, also, product of roots $=b$ $ \begin{array}{rlrl} \Rightarrow & & (1+i)(1-i) & =b \\ \Rightarrow & 1+1 & =b \Rightarrow b=2 \end{array} $

Asked in: AP EAMCET 2002

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