Solve the quadratic

Adam Zettel · September 22, 2026 · written with an agent

A ball is thrown straight up at 4 m/s from 1 m above the ground. When does it land? Write roots(a, b, c), the two solutions of $a x^{2} + b x + c = 0$ , smaller first.

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A ball is thrown straight up at 4 m/s from 1 m above the ground. With $g$ rounded to 10 m/s², its height after $t$ seconds is

y (t) = 1 + 4 t - 5 t^{2} .

It lands when $y (t) = 0$ , that is, when $- 5 t^{2} + 4 t + 1 = 0$ .

Write roots(a, b, c), the two solutions of $a x^{2} + b x + c = 0$ , smaller first. You may assume $b^{2} \geq 4 a c$ . The tests use the ball and a rectangle with a perimeter of 10 and an area of 6, whose sides $x$ and $5 - x$ satisfy $x^{2} - 5 x + 6 = 0$ .

Your task

Write this function:

roots(a, b, c): The two roots of the quadratic with coefficients a, b and c, smaller first.

Make these tests pass 2 of 2 fail

$x^2 - 5x + 6 = 0$ gives 2 and 3 assert_near: |0 - 2| = 2 > 1e-12 (and 1 more) (fails)
$-5t^2 + 4t + 1 = 0$ gives -0.2 and 1, smaller first assert_near: |0 - -0.2| = 0.2 > 1e-12 (and 1 more) (fails)

Printed

t1: 0 t2: 0

Your task

Solutions 1