HardMathematicsHigh School (9–10)GeneralAlgebra › Quadratic EquationsNumericalword problem

A stone is thrown upwards. After t seconds its height is h = 30t - 5t² metres.

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A stone is thrown upwards. After $t$ seconds its height is $h = 30t - 5t^2$ metres. At what times is it $25\ \text{m}$ above the ground? Explain why there are two answers.

Need a reminder? The key ideaShow

The roots of $ax^2 + bx + c = 0$ , with $a \neq 0$ , are $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ . Read $a$ , $b$ and $c$ with their signs, work out $b^2 - 4ac$ first, and check each root in the problem.

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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A stone is thrown upwards. After t seconds its height is h = 30t - 5t² metres.

The worked solution

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