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

1 Answer
Apr 26, 2018

Answer:

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!