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

1 Answer
Alan P.
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

Related questions
See all questions in Solutions Using the Discriminant
Impact of this question
1841 views around the world
You can reuse this answer
Creative Commons License