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

1 Answer
Guillaume L.
Apr 26, 2018

In RR, there's no solution for this equation.
In CC, z_"1"=2-isqrt(6)
z_"2"=2+isqrt(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 RR, there's no solution for this equation.

Else, in CC:
Let : δ²=Δ
δ=2isqrt(6)
So: z_"1"=(-b-δ)/(2a),
z_"2"=(-b+δ)/(2a)
z_"1"=2-isqrt(6)
z_"2"=2+isqrt(6)
\0/ here's our answer!

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