The zeros of the function f(x) = x2 + 5x + 5 is [tex]\rm x=\dfrac{-5\pm\sqrt{5}}{2}[/tex]correct option is c.
Roots of the quadratic equation
The zeros of the quadratic equation are determined by using the quadratic formula;
[tex]\rm x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
Given information
Function; [tex]\rm f(x)=x^2+5x+5\\\\[/tex]
On comparing with the given equation
The value of a = 1, b = 5, and c = 5.
Substitute all the values in the formula;
[tex]\rm x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}\\\\\rm x=\dfrac{-5\pm\sqrt{5^2-4(1)(5)} }{2(1)}\\\\\rm x=\dfrac{-5\pm\sqrt{25-20} }{2}\\\\x=\dfrac{-5\pm\sqrt{5} }{2}[/tex]
Hence, the zeros of the function f(x) = x2 + 5x + 5 is [tex]\rm x=\dfrac{-5\pm\sqrt{5}}{2}\\\\[/tex].
To know more about quadratic equations click the link given below.
https://brainly.com/question/2263981
