Find the zeros of the function algebraically.
$f ( x ) = \sqrt { 5 x + 2 }$
A) $\frac { 5 } { 2 }$
B) $- 2$
C) $- \frac { 2 } { 5 }$
D) $\frac { 2 } { 5 }$
E) $- \frac { 5 } { 2 }$

Question

Find the zeros of the function algebraically. 
$f ( x ) = \sqrt { 5 x + 2 }$
A) $\frac { 5 } { 2 }$
B) $- 2$
C) $- \frac { 2 } { 5 }$
D) $\frac { 2 } { 5 }$
E) $- \frac { 5 } { 2 }$

Quizplus · Accepted Answer

To find the zeros of the function, we need to solve the equation $\sqrt{5x+2}=0$. However, since the square root of any number is always non-negative, the only way for the function to be equal to zero is if the expression inside the square root is equal to zero. Therefore, we need to solve the equation $5x+2=0$. 
\begin{align*}
5x+2&=0 \
5x&=-2 \
x&=-\frac{2}{5}
\end{align*}
So $x=-\frac{2}{5}$ is one of the zeros. However, since the square root of a positive number can never be negative, there can be no other real zeros for $f(x)$. Therefore, the only other answer choice that could possibly be correct is E) $-\frac{5}{2}$. To check whether $x=-\frac{5}{2}$ is a zero of the function, we substitute it into the function: 
\begin{align*}
f\left(-\frac{5}{2}ight)&=\sqrt{5\left(-\frac{5}{2}ight)+2} \
&=\sqrt{-\frac{23}{2}} \
\end{align*}
Since the square root of a negative number is not a real number, $x=-\frac{5}{2}$ is not a zero of the function. Therefore, the correct answer is C) $-\frac{2}{5}$ only.

Find the Zeros of the Function Algebraically f(x)=5x+2f ( x ) = \sqrt { 5 x + 2 }f(x)=5x+2​

Find the Zeros of the Function Algebraically $f ( x ) = \sqrt { 5 x + 2 }$