Question

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

Answer 1

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