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.

Question

asked Oct 8, 2023 87.9k views

1 Answer

Yoon · Answer 1 · 2023-10-13T01:15:37+0000

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.