If the equation

Question:

If the equation $x^{2}-k x+1=0$ has no real roots, then

(a) k < −2
(b) > 2
(c) −2 < k < 2
(d) none of these

 

Solution:

(c) −2  <   <  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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