Notebooks · posts/solve-the-quadratic

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.

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 $x^{2} - 5 x + 6 = 0$ .

Look inside this program

Atlas
The program’s map: every function and which calls which.
There’s no recorded run of this program yet.

This is a problem: its tests fail until the functions in it are written. Edit a cell and run it to try; the cells below it show whether the tests pass.

Shift+Enter in a cell runs it and moves to the next. Running a cell runs every cell above it too, as one program.

[1]lines 20–40

#| The two roots of the quadratic with coefficients a, b and c, smaller first.
def roots(a, b, c) {
    return 0.0, 0.0
}

t1, t2 = roots(-5, 4, 1)
show t1, t2

test "$x^2 - 5x + 6 = 0$ gives 2 and 3" {
    x1, x2 = roots(1, -5, 6)
    assert_near(x1, 2.0, 1.0e-12)
    assert_near(x2, 3.0, 1.0e-12)
}
test "$-5t^2 + 4t + 1 = 0$ gives -0.2 and 1, smaller first" {
    t1, t2 = roots(-5, 4, 1)
    assert_near(t1, -0.2, 1.0e-12)
    assert_near(t2, 1.0, 1.0e-12)
}

# SPDX-License-Identifier: MIT OR Apache-2.0
# SPDX-FileCopyrightText: 2026 The Viv authors