Question

For what values of k, the roots the equation $x^2-kx+1=0$ are imaginary?

Answer 1

$$\begin{gathered} \begin{array}{l}\text{It is given that the roots of the equation (}{x}^2\text{-}kx+1=0)\text{are imaginary.}\\ \text{Here,}a=1,b=-k\mathrm{and}c=1\end{array} \\ \therefore b^2-4ac<0 \\ \Rightarrow k^2-4\times 1\times 1<0 \\ \Rightarrow k^2<4 \\ \Rightarrow k^2-4<0 \\ \Rightarrow (k+2)(k-2)<0 \\ \Rightarrow -2<k<2 \end{gathered}$$