Question

If the equation x2-x+1=0 does not possess real roots, then​

Answer 1

Given:

A quadratic equation: $x^{2} - x +1 = 0$  ..............(1)

To Find:

Condition for the quadratic equation to possess non-real roots =?

Step-by-step explanation:

For a quadratic equation to have non-real roots its determinant should be equal to 0.

For the equation $ax^{2} + bx +c = 0$   ..............(2)

Determinant = D = $\sqrt{b^{2} - 4ac }$

On comparing (1) and (2)

Determinat for (1) = D = $\sqrt{(-1)^{2} - 4 }$ = $\sqrt{-3}$

since D = $i\sqrt{3}$    where, i = $\sqrt{-1}$

D is not greater than equal to 0.

Hence, the roots of the equation (1) and non-real.