How do you solve using the quadratic formula x^2-4x+10=0?

2 Answers
May 3, 2015

Given a quadratic equation of the form
ax^2+bx+c=0
the quadratic roots can be evaluated using the formula
x=(-b+-sqrt(b^2-4ac))/(2a)

For x^2-4x+10 = 0

x= (4+-sqrt(16-40))/2

x= 2+-sqrt(-6)

This equation has no Real solutions
but if we are allowed Complex solutions:
x=2+-sqrt(6)i

May 4, 2015

You notice the 1st degree coefficient is even, so you can use the direct formula
P(x)=ax^2+bx+c, β=b2
x1,x2={−β±sqrt(β^2−ac)}/a
so x_1,x_2=2±sqrt(4−10)=2±sqrt(−6)
So you know there are no solutions in ℝ, and you have the complex conjugated solutions z=2+sqrt(6)i andbarz=2−sqrt(6)i