Question

How do you find the discriminant of `x^2-2x+1=0` and use it to determine if the equation has one, two real or two imaginary roots?

Answer 1

`Delta =0 ->` equation has a one real solution `x=1`

Explanation:

Consider the general form of the quadratic equation:

`ax^2+bx+c=0`

The discriminant `(Delta)` is defined as: `b^2-4ac`

Three cases arise:

(i) `Delta >0 ->` the equation has two distinct real roots
(ii) `Delta <0 ->` the equation has two complex roots
(iii) `Delta =0 ->` the equation has one real solution (Strictly, two equal real roots)

In our equation: `x^2-2x+1=0`

`Delta = (-2)^2-4*1*1 = 4-4 =0`

Hence the equation has one real solution.

The equation may be factorised as: `(x-1)(x-1)=0`

Hence the only real solution is `x=1`