#### Answer

x-intercepts: $-5$ and $5$
y-intercepts: $-2$ and $2$

#### Work Step by Step

RECALL:
(1) A point where the graph touches or crosses the x-axis is called an x-intercept. Given an equation, the x-intercept/s can be found by setting $y=0$ then solving for $x$.
(2) A point where the graph touches or crosses the y-axis is called a y-intercept.
Given an equation, the y-intercept/s can be found by setting $x=0$ then solving for $y$.
Solve for the x-intercept/s by setting $y=0$ then solving for $x$:
$\begin{array}{ccc}
&4x^2+25y^2 &= &100
\\&4x^2+25(0^2) &= &100
\\&4x^2 &= &100
\\&\dfrac{4x^2}{4} &= &\dfrac{100}{4}
\\&x^2 &= &25
\\&x &= &\pm\sqrt{25}
\\&x &= &\pm\sqrt{5^2}
\\&x &= &\pm 5
\end{array}$
The x-intercepts are $-5$ and $5$.
Solve for the y-intercept/s by setting $x=0$ then solving for $y$:
$\begin{array}{ccc}
&4x^2+25y^2 &= &100
\\&4(0^2)+25y^2 &= &100
\\&25y^2 &= &100
\\&\dfrac{25y^2}{25} &= &\dfrac{100}{25}
\\&y^2 &= &=4
\\&y &= &\pm\sqrt{4}
\\&y &= &\pm\sqrt{2^2}
\\&y &= &\pm 2
\end{array}$
The y-intercepts are $-2$ and $2$.