Question 241727
The discriminant is the b^2-4ac part of the quadratic formula

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 

Rearranging the equation to standard ax^2+bx+c=0 form gives:

27x^2-18x+3 = 0

So the discrimant is {{{-18^2 - 4*27*3 = 0}}}

This tells us that there is only one root ie the graph only crosses the x axis once.

The graph confirms this {{{ graph( 300, 200, -6, 5, -10, 10, 27x^2-18x+3) }}} 

The type of solution is determined by {{{sqrt(b^2-4ac)}}}. If this is a whole number then the solution is said to be rational. The square root of zero is zero. This means that the solution is rational because zero can be represented by a fraction a/b where b is not equal to zero.

Does this help?

Any questions?