intercepts of y=x^2+x+1 — step-by-step solution

On the horizontal axis, y = 0: solve

x^{2} + x + 1 = 0

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 - 4 \cdot 1 \cdot 1

Δ = 1 - 4

ⓘ Start from

1

and move back

4

on the number line, going below zero:

1 - 4

-3

Δ = -3

Δ < 0

, the equation has no real root.

Solution:

x \in \emptyset

On the vertical axis, x = 0: calculate f(0)

⇥

0^{2} + 0 + 1

⇥ⓘ Adding 0 changes nothing:

0 + 0 + 1

1

⇥

1

▶Axis intercepts:

(0, 1)