Question

5x^2 - 5x + 6 = 0.Is this solution:(A) Two distinct rational solutions.(B) Two distinct irrational solutions.(C) Two complex solutions.(D) Single rational solution.

Answer 1

To determine the number and type of solutions, we use the general formula:

`x=(-b\pm√(b^2-4ac))/(2a).`

In the given equation:

`\begin{gathered} a=5, \\ b=-5, \\ c=6. \end{gathered}`

Therefore:

`x=(5\pm√(25-120))/(10).`

From the determinant, we notice that the equation has complex solutions because it is negative.

Answer: Two complex solutions.