How do you find the discriminant, describe the number and type of root, and find the exact solution using the quadratic formula given #x^2-2x+5=0#?

1 Answer
Dec 17, 2016

Answer:

Discriminant: #(-16)#
There are no roots (i.e. no solutions in terms of Real numbers)

Explanation:

For the general case: #ax^2+bx+c=0#

The discriminant is #Delta = b^2+4ac#

There are #{("zero roots"," if ",Delta < 0),("one root"," if ",Delta=0),("2 roots"," if ",Delta > 0):}#

The solution(s) if it/they exist are given by the quadratic formula:

#x=(-b+-sqrt(Delta))/(2a)#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

For the given example: #x^2-2x+5=0#
#color(white)("XXX")#i.e. #a=1, b=(-2),c=5#

#Delta=(2^2-4*1*5) = -16#

and since #Delta < 0#
#color(white)("XXX")#this equation has no solutions.