Question

What are the zeros of the function f(x) = x2 + 5x + 5 written in simplest radical form?



Quadratic formula: x = StartFraction negative b plus or minus StartRoot b squared minus 4 a c EndRoot Over 2 a EndFraction

x = StartFraction 5 plus or minus 10 StartRoot 5 EndRoot Over 2 EndFraction
x = StartFraction negative 5 plus or minus 10 StartRoot 5 EndRoot Over 2 EndFraction
x = StartFraction negative 5 plus or minus StartRoot 5 EndRoot Over 2 EndFraction
x = StartFraction 5 plus or minus StartRoot 5 EndRoot Over 2 EndFraction

Answer 1

To find the zeros of the quadratic function \( f(x) = x^2 + 5x + 5 \), we can use the quadratic formula:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

where \( a = 1 \), \( b = 5 \), and \( c = 5 \).

1. First, calculate the discriminant (\( b^2 - 4ac \)):
\[
b^2 = 5^2 = 25
\]
\[
4ac = 4 \cdot 1 \cdot 5 = 20
\]
\[
b^2 - 4ac = 25 - 20 = 5
\]

2. Now, substitute \( a \), \( b \), and the discriminant into the quadratic formula:
\[
x = \frac{-5 \pm \sqrt{5}}{2 \cdot 1}
\]

3. Simplifying gives:
\[
x = \frac{-5 \pm \sqrt{5}}{2}
\]

Thus, the zeros of the function \( f(x) = x^2 + 5x + 5 \) in simplest radical form are:

\[
x = \frac{-5 \pm \sqrt{5}}{2}
\]

The appropriate answer from your given options is:

- \( x = \frac{-5 \pm \sqrt{5}}{2} \)