Question

The answer to this word problem usinf discriminant

Answer 1

$\bf h=-9.8t^2+45t+1.2\implies 64.5=-9.8t^2+45t+1.2 \\\\\\ 0=-9.8t^2+45t-63.3\\\\ -------------------------------$

$\bf \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ 0=\stackrel{\stackrel{a}{\downarrow }}{-9.8}t^2\stackrel{\stackrel{b}{\downarrow }}{+45}t\stackrel{\stackrel{c}{\downarrow }}{-63.3} ~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases} \\\\\\ (45)^2-4(-9.8)(-63.3)\implies -456.36$

the discriminant is a negative value, thus no solution for such quadratic, meaning if we use h=64.5 like we did, there's no "t" seconds at which point the ball hits the batting cage.