Question:
If the equation $x^{2}-a x+1=0$ has two distinct roots, then
(a) $|a|=2$
(b) $|a|<2$
(c) $|a|>2$
(d) None of these
Solution:
The given quadric equation is $x^{2}-a x+1=0$, and roots are distinct.
Then find the value of $a$.
Here, $a=1, b=a$ and,$c=1$
As we know that $D=b^{2}-4 a c$
Putting the value of $a=1, b=a$ and, $c=1$
$=(a)^{2}-4 \times 1 \times 1$
$=a^{2}-4$
The given equation will have real and distinct roots, if $D>0$
$a^{2}-4>0$
$a^{2}>4$
$a>\sqrt{4}$
$>\pm 2$
Therefore, the value of $|a|>2$
Thus, the correct answer is (c)
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