How do you find the discriminant and how many solutions does #1= -9x + 11x^2# have?

1 Answer
May 5, 2015

For a quadratic equation in standard form: #ax^2+bx+c=0#
the discriminant is #Delta = b^2-4ac#

First rearrange the given equation into standard form
#1= -9x+11x^2#

11x^2-9x -1 =0#

Evaluate the discriminant:
#Delta = (-9)^2 -4(11)(-1)#
#= 81+44 = 125#

Since the solutions to a quadratic can be evaluated by the formula
#x=(-b+-sqrt(Delta))/(2a)#
It follows that
#Delta { (< 0 rarr "no Real solutions"),(=0rarr "1 Real solution"),(>0rarr "2 Real solutions") :}#

For this example, #Delta >0#
therefore there are 2 Real solutions