Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions.
x^2 = 5x + 6

Question

Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions.
x^2 = 5x + 6

anonymous · Answer

For this you use the quadratic formula. The discriminant is the part under the radical:

$$\sqrt{b ^{2}-4ac}$$

If you take your equation and make it so that it equals 0, you receive:

x^2-5x-6

From that, a = 1, b = -5, and c = -6.

If you put that into the equation above, what do you get?