What is the discriminant of $x^2+x+1=0$ and what does that mean?

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Answer 1 · 2015-07-16T19:41:33

The discriminant is -3. It tells you that there are no real roots, but there are two complex roots to the equation.

If you have a quadratic equation of the form

$ax^2+bx+c=0$

The solution is

$x = (-b±sqrt(b^2-4ac))/(2a)$

The discriminant $Δ$ is $b^2 -4ac$ .

The discriminant "discriminates" the nature of the roots.

There are three possibilities.

Your equation is

$x^2 +x +1 = 0$

$Δ = b^2 – 4ac = 1^2 - 4×1×1 = 1 – 4 = -3$

This tells you that there are no real roots, but there are two complex roots.

We can see this if we solve the equation.

$x^2 +x +1 = 0$

$x = (-b±sqrt(b^2-4ac))/(2a) = (-1±sqrt(1^2 - 4×1×1))/(2×1) = (-1±sqrt(1-4))/2 = (-1 ±sqrt(-3))/2 = 1/2(-1±isqrt3) =-1/2(1±isqrt3)$

$x =—1/2(1+ isqrt3)$ and $x = -1/2(1- isqrt3)$

What is the discriminant of x^2+x+1=0x^2+x+1=0 and what does that mean?