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# If $\;1-i\;$ is a root of the equation $\;x^{2} + bx + c=0\;$ where $\;a,b \in R\;$ , then find the values of a and b .

$(a)\;2,3\qquad(b)\;0,2\qquad(c)\;-2,2\qquad(d)\;4,-2$

Explanation :
Sum of roots $\; \large\frac{-a}{1} = (1-i)+(1+i)$
$a=-2$
(Since non real complex roots occur in conjugate pairs )
Product of roots $\;\large\frac{b}{1}=(1-i)(1+i)$ => $\;b=2$