what are the zeros of the function $f(x)=x^{2}+5x + 5$ written in simplest radical form?\nquadratic formula…

what are the zeros of the function $f(x)=x^{2}+5x + 5$ written in simplest radical form?\nquadratic formula: $x=\frac{-bpmsqrt{b^{2}-4ac}}{2a}$\n$x = \frac{5pm10sqrt{5}}{2}$\n$x=\frac{-5pm10sqrt{5}}{2}$\n$x=\frac{-5pmsqrt{5}}{2}$\n$x=\frac{5pmsqrt{5}}{2}$

what are the zeros of the function $f(x)=x^{2}+5x + 5$ written in simplest radical form?\nquadratic formula: $x=\frac{-bpmsqrt{b^{2}-4ac}}{2a}$\n$x = \frac{5pm10sqrt{5}}{2}$\n$x=\frac{-5pm10sqrt{5}}{2}$\n$x=\frac{-5pmsqrt{5}}{2}$\n$x=\frac{5pmsqrt{5}}{2}$

Answer

Explanation:

Step1: Identify coefficients

For the quadratic function $f(x)=x^{2}+5x + 5$, we have $a = 1$, $b=5$, $c = 5$.

Step2: Substitute into quadratic formula

Substitute $a$, $b$, $c$ into $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$, we get $x=\frac{-5\pm\sqrt{5^{2}-4\times1\times5}}{2\times1}$.

Step3: Simplify the expression

First, calculate the value inside the square - root: $5^{2}-4\times1\times5=25 - 20=5$. Then the formula becomes $x=\frac{-5\pm\sqrt{5}}{2}$.

Answer:

$x=\frac{-5\pm\sqrt{5}}{2}$ (corresponds to the third option)