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
Discriminant:
There are no roots (i.e. no solutions in terms of Real numbers)
Explanation:
For the general case:
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:
#Delta=(2^2-4*1*5) = -16#
and since