If \(1-i\), is a root of the equation \({x^2} + ax + b = 0\), where \(a,b \in R\), then the values of \(a\) and \(b\) are,
Practice this Quadratic Equation question from Engineering Entrance Exam.
Question Details
Mathematics
Quadratic Equation
Engineering Entrance Exam
Question
If \(1-i\), is a root of the equation \({x^2} + ax + b = 0\), where \(a,b \in R\), then the values of \(a\) and \(b\) are,
Solution
Since complex roots always occur in conjugate pair.
\(\therefore \) Other conjugate root is \(1+i\).
Sum of roots \( = \frac{{ - a}}{1} = (1 - i) + (1 + i)\)
\( \Rightarrow a = - 2\)
Product of roots \( = \frac{{ b}}{1} = (1 - i)(1 + i)\)
\( \Rightarrow b = 2\)