Chapter 2 - Linear and Quadratic Functions - Section 2.3 Quadratic Functions and Their Zeros - 2.3 Assess Your Understanding - Page 146: 20

the zeros are $x=-5$ or $x=5$ and the $x$-intercepts are $(-5,0)$ and $(5,0)$.

By factorization, we have $$ H(x)=2x^2-50=2(x^2-25)=2(x+5)(x-5) .$$ That is, we have $x+5=0 $ or $x-5=0$. So the zeros are $x=-5$ or $x=5$ and the $x$-intercepts are $(-5,0)$ and $(5,0)$.