Question:
If the equation $x^{2}-k x+1=0$ has no real roots, then
(a) k < −2
(b) k > 2
(c) −2 < k < 2
(d) none of these
Solution:
(c) −2 < k < 2
It is given that the equation $x^{2}-k x+1=0$ has no real roots.
$\therefore\left(b^{2}-4 a c\right)<0$
$\Rightarrow(-k)^{2}-4 \times 1 \times 1<0$
$\Rightarrow k^{2}<4$
$\Rightarrow-2
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