What is the discriminant of #-9x^2+10x=-2x+4# and what does that mean?

1 Answer
Jul 22, 2015

Answer:

#0#
It means that there is exactly 1 Real solution for this equation

Explanation:

The discriminant of a quadratic equation is #b^2 – 4ac#. To calculate the discriminant of the equation you provided, we move #-2x# and #4# to the left, resulting in #-9x^2+12x-4#. To calculate the discriminant of this simplified equation, we use our formula above, but substitute #12# for #b#, #-9# as #a#, and #-4# as #c#.

We get this equation: #(12)^2 - 4(-9)(-4)#, which evaluates to #0#

The "meaning" is the result of the discriminant being a component of the quadratic formula for the solution(s) to quadratic equation in the form:
#color(white)("XXXX")##ax^2+bx+c=0#
where the solutions can be determined by:
#color(white)("XXXX")##x=(-b+-sqrt(b^2-4ac))/(2a)#

Notice that the discriminant is the component within the square root, and as a result:
#"discriminant" { (= 0, " one Real root"), (< 0, " no Real Roots"), (> 0, " two Real roots") :}#