Question

x^2-6x+25=0

Answer 1

x^2 -6x+25=0
Per quadratic formula, roots of ax^2+bx+c are
x=[-b+sqrt(b^2-4ac)]/2a and x=[-b-sqrt(b^2-4ac)]/2a


In this example, a=1, b=-6, and c=25
So, x= [6+sqrt(36-100)]/2 and x= [6-sqrt(36-100)]/2
=> x = [6+sqrt(-64)]/2 and x = [6-sqrt(-64)]/2
=> x = 3+4i and x= 3-4i

Answer 2

The radicand of the quadratic formula is called
the Discriminant \(\Delta =b^2-4ac\)

if \(\Delta=0\) there is two equal solutions
if \(\Delta>0\) there are two different solutions
if \(\Delta<0\) there are no real solutions (complex solutions only)