x^2-x+1>0 — step-by-step solution

Let's solve in

ℝ

x^{2} - x + 1 > 0

Given the quadratic form

a x^{2} + b x + c

, you can calculate the discriminant:

Δ = b^{2} - 4 a c

. Here

a = 1

b = -1

and

c = 1

Δ = {(-1)}^{2} - 4 \cdot 1 \cdot 1

ⓘ Powers are computed before multiplications, additions and subtractions. An integer power is a repeated product:

{(-1)}^{2}

(-1) \cdot (-1)

1

Δ = 1 - 4

ⓘ Start from

1

and move back

4

on the number line, going below zero:

1 - 4

-3

Δ = -3

The quadratic has no real root: it has the sign of a =

1

everywhere, so it is indeed positive for every

x

▶Solution found:

x \in ℝ