How do you find the discriminant and how many solutions does #h(x)=x^2-2x-35# have?

1 Answer
May 10, 2015

Solutions to a quadratic of the form #ax^2+bx+c=0# are given by
the quadratic formula #(-b+-sqrt(b^2-4ac))/(2a)#

The sub-expression within the square root determines the number (and type) of solutions; this sub-expression is called the "discriminant" and is typically expressed as:
#Delta = b^2-4ac#
with the conditions
#Delta { (< 0 " there are no Real solutions"),(=0" there is 1 Real solution"),(>0" there are 2 Real solutions"):}#

Given #h(x) = x^2-2x-35#

#Delta = (-2)^2 -4(1)(-35)#
#= 4+140 = 144#
# >0#
so there are two Real solutions