# If the equation x2 − ax + 1 = 0 has two distinct roots, then

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)