Find all vertical asymptotes of the following function. f(x)=(5x^2-21x+4)/(2x-8) square v

To find the vertical asymptotes of the function \( f(x) = \frac{5x^2 - 21x + 4}{2x - 8} \), we need to determine where the denominator is equal to zero, as these are the points where the function is undefined and potentially has vertical asymptotes.<br /><br />Set the denominator equal to zero and solve for \( x \):<br /><br />\[ 2x - 8 = 0 \]<br /><br />Add 8 to both sides:<br /><br />\[ 2x = 8 \]<br /><br />Divide both sides by 2:<br /><br />\[ x = 4 \]<br /><br />So, the vertical asymptote of the function \( f(x) = \frac{5x^2 - 21x + 4}{2x - 8} \) is at \( x = 4 \).<br /><br />Therefore, the vertical asymptote is:<br /><br />\[ \boxed{4} \]