Question

If the equation $x^2-kx+1=0$ has no real roots, then
(a) k < −2
(b) k > 2
(c) −2 < k < 2
(d) none of these

Answer 1

(c) −2 < k < 2

$$\begin{gathered} \text{It is given that the equation}{x}^2-kx+1=0\text{has no real roots.} \\ \therefore (b^2-4ac)<0 \\ \Rightarrow {(-k)}^2-4\times 1\times 1<0 \\ \Rightarrow k^2<4 \\ \Rightarrow -2<k<2 \end{gathered}$$