Answer:
C. [tex]x=\frac{5}{2}[/tex]
Step-by-step explanation:
The quadratic formula is:
[tex]x_{1,2}=\frac{-b\±\sqrt{b^{2}-4ac}}{2a}[/tex]
Where [tex]a[/tex] is the coefficient of the quadratic team. [tex]b[/tex] is the coefficient of the linear term, and [tex]c[/tex] is the independent term.
So, the given equation is:
[tex]x^2 - 5x + \frac{25}{4} = 0[/tex]
Where:
[tex]a=1\\b=-5\\c=\frac{25}{4}[/tex]
[tex]x_{1,2}=\frac{-(-5)\±\sqrt{(-5)^{2}-4(1)(\frac{25}{4} )}}{2(1)}\\x_{1,2}=\frac{5\±\sqrt{25-25}}{2}\\x_{1,2}=\frac{5\±\sqrt{0}}{2}\\x_{1,2}=\frac{5}{2}[/tex]
This means that the equation has a unique solution.
Therefore, the right answer is C.
