factoring quadratics - A stone is projected vertically upwards. Its height h meters after time t seconds is given by the equation: h = 60t − 5t2 After how many seconds is its height equal to 135 meters?

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factoring quadratics quadratic equations

Anonymous

rupa Reddy (last edited 2 years ago) (Teacher, UG1 Grade)

Put h = 135:

⇒ 135 = 60t − 5t²

⇒ 5t² − 60t + 135 = 0⇒ t² − 12t + 27 = 0

⇒ (t − 3)(t − 9) = 0⇒ t = 3 or 9

Thus its height is 135 meters after 3 seconds and again after 9 seconds.

(i.e. once on the way up and once on the way down after it has reached its maximum height)