How do you find the discriminant and how many solutions does x^2-4x+10=0 have?

Apr 26, 2018

Answer:

In $\mathbb{R}$, there's no solution for this equation.
In $\mathbb{C}$, ${z}_{\text{1}} = 2 - i \sqrt{6}$
${z}_{\text{2}} = 2 + i \sqrt{6}$

Explanation:

x²-4x+10=0
It's the standard form of ax²+bx+c=0, so we have to find the discriminant Δ.
Δ=b²-4ac, where : $a = 1$, $b = - 4$, $c = 10$
=(-4)²-4*1*10
$= 16 - 40$
$= - 24$
So, in $\mathbb{R}$, there's no solution for this equation.

Else, in $\mathbb{C}$:
Let : δ²=Δ
δ=2isqrt(6)
So: z_"1"=(-b-δ)/(2a),
z_"2"=(-b+δ)/(2a)
${z}_{\text{1}} = 2 - i \sqrt{6}$
${z}_{\text{2}} = 2 + i \sqrt{6}$
\0/ here's our answer!