Question

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

Answer 1

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!