SOLUTION: I am supposed to determine the nature of the solutions of the equation. Determine whther there is one real solution, two real solutions, or two non real solutions. x^2 - 3x +8 =

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I am supposed to determine the nature of the solutions of the equation. Determine whther there is one real solution, two real solutions, or two non real solutions. x^2 - 3x +8 =      Log On


   

Question 232608: I am supposed to determine the nature of the solutions of the equation. Determine whther there is one real solution, two real solutions, or two non real solutions.
x^2 - 3x +8 =0
There is two real solutions?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
The general form of a quadratic equation:
ax%5E2+%2B+bx++%2B+c+=+0
The quadratic formula:
x+=+%28-b+%2B-+sqrt%28b%5E2+-4ac%29%29%2F%282a%29

The expression inside the square root, b%5E2-4ac, is called the discriminant. It is called this because its value determines whether there are 0, 1 or 2 real roots. This is how it works:
  • The discriminant is a positive number (any positive number. Since the discriminant is inside the square root we will find the square root of the discriminant. The square root of a positive number is another positive number. And since this square root is both added to and subtracted from -b in the numerator, we will end up with 2 real roots: one when we add the square root and one when we subtract.
  • The discriminant is zero. The square root of zero is zero. And whether you add zero to -b or subtract zero from -b you end up with the same thing, -b. This is when we get 1 real root.
  • The discriminant is a negative number (any negative number). Since it is impossible to square a real number and get a negative number, the square root of any negative number does not exist within the set of Real numbers. This is when we get no real roots.

Using this on you equation...
Find the value of the discriminant:
b%5E2+-+4ac+=+%28-3%29%5E2+-+4%281%29%288%29+=+9+-+32+=+-23
The discriminant is a negative number so there are no real roots.