SOLUTION: The value of the discriminant is ________? 27x² = 18x – 3 How many solutions are there? Are they a) rational? b) Irrational c) Imaginary solutions?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: The value of the discriminant is ________? 27x² = 18x – 3 How many solutions are there? Are they a) rational? b) Irrational c) Imaginary solutions?       Log On


   

Question 241727: The value of the discriminant is ________?
27x² = 18x – 3
How many solutions are there?
Are they a) rational?
b) Irrational
c) Imaginary solutions?
Answer by JimboP1977(311) About Me  (Show Source):
You can put this solution on YOUR website!
The discriminant is the b^2-4ac part of the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
Rearranging the equation to standard ax^2+bx+c=0 form gives:
27x^2-18x+3 = 0
So the discrimant is -18%5E2+-+4%2A27%2A3+=+0
This tells us that there is only one root ie the graph only crosses the x axis once.
The graph confirms this +graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+27x%5E2-18x%2B3%29+
The type of solution is determined by sqrt%28b%5E2-4ac%29. 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?