Question

If the equation x² − bx + 1 = 0 does not possess real roots, then

पर्याय

• −3 < b < 3

• −2 < b < 2

• b > 2

• b < −2

Answer 1

The given quadric equation is `x^2 - bx + 1 = 0`, and does not have real roots.

Then find the value of b.

Here,  a = 1, b = -b and ,c = 1

As we know that `D = b^2 - 4ac`

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

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

`=b^2 - 4`

The given equation does not have real roots, if D < 0 

`b^2 - 4 < 0`

`b^2 < 4`

`b< sqrt4`

`b< ±2`

Therefore, the value of -2 < b< 2 .