Question

a ball is hit into the air; its height, in metres. after t seconds is h = -5^2 + 30t + 1 for how long is the ball in the air?

how do i find the x intercepts when it cannot be factored?

Answer 1

somethings missing in this. is the ball hit at inclined angle , something like projectile motion. Then it should have t^2 term in it, the path being parabolic. you should get two values of t for each height, one is the time when it reaches height while going up and the other time while going down through the same height

Answer 2

I'm assuming you meant:
\[h(t)= -5t^2 + 30t + 1 \]
\[0= -5t^2+30t+1\]
\[0=t^2-6t-\frac15\]
\[\frac{46}5 = t^2 - 6t +9\]
\[\frac{46}5 = (t-3)^2\]
\[t= \frac15(15\pm\sqrt{230})\]
\[t\approx-0.0331; \space\space\space t\approx 6.0331\]