Question

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

Options

• |a| = 2

• |a| < 2

• |a| > 2

• None of these

Answer 1

The given quadric equation is x² − ax + 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 - 4ac`

Putting the value of a =1,b = a and, c = 1

`=(a)^2 - 4 xx 1 xx 1`

` = a^2 - 4`

The given equation will have real and distinct roots, if D > 0

 `a^2-  4 > 0`

         `a^2 > 4`

          ` a > 4`

          `a > sqrt4`

            `> ± 2`

Therefore, the value of |a| > 2.