---
title: "Algebra 1 – Roots of Quadratic Equations"
id: 51703
type: "computer_media"
slug: "algebra-1-roots-of-quadratic-equations"
url: "http://localhost/computer_media/algebra-1-roots-of-quadratic-equations/"
markdown_url: "http://localhost/computer_media/algebra-1-roots-of-quadratic-equations.md"
published_at: "2023-08-13T23:14:28+00:00"
modified_at: "2026-04-02T15:59:38+00:00"
author: "David Anderson"
featured_image:
  url: "http://localhost/wp-content/uploads/2019/02/20230809-041332.jpg"
excerpt: "Solve any quadratic equation instantly — real or complex roots displayed with full imaginary-number notation, plus input validation and repeat-solve looping."
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  - name: "TS 1000"
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media_type: "Cassette"
download_url: "https://archive.org/download/timex-sinclair-software-archive/Algebra 1 - Roots of Quadratic Equations (198x)(Timex)(TS1000)(Cassette).zip"
mediadate: "198x"
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---

This program solves quadratic equations of the form AX² + BX + C = 0, computing both real and complex roots using the quadratic formula. It calculates the discriminant (B²−4AC) stored in variable S, then uses SQR(ABS S) to safely extract the square root regardless of sign, branching at line 70 to handle the complex-root case. For real roots, both solutions are printed directly; for complex roots, the real part (−B/2A) and imaginary part (R/2A) are displayed separately with “I” notation. The program uses SLOW mode for user interaction and FAST mode during calculation, and validates that coefficient A is non-zero before proceeding.

***

## Program Analysis

### Program Structure

The program flows through four distinct phases: input collection (lines 10–46), discriminant calculation (lines 47–60), root display (lines 70–110), and repeat-or-quit logic (lines 110–160). Lines 170–180 are a save/restart stub that is never reached during normal execution.

1. **Lines 10–46:** Display the equation form, collect coefficients A, B, and C with inline echo-printing, and validate that A ≠ 0.
2. **Lines 47–60:** Switch to FAST mode, compute discriminant `S = B*B - 4*A*C`, and compute `R = SQR(ABS S)`.
3. **Lines 70–110:** Branch on the sign of S; print real roots or complex conjugate pair accordingly.
4. **Lines 110–160:** Prompt for another calculation; accept “Y” to restart via `RUN` or “N” to `STOP`, with a fallback message for other input.

### Mathematical Approach

The discriminant `S = B² − 4AC` is computed at line 50. Taking `SQR(ABS S)` at line 60 avoids a runtime error when S is negative (which would otherwise cause a square-root-of-negative error), storing the magnitude of the root in `R`. The sign of S is then tested at line 70 to decide which formula to apply.

For real roots (S ≥ 0), the two solutions are printed inline at line 85 as `(-B-R)/(2*A)` and `(R-B)/(2*A)`. For complex roots (S < 0), line 102 repurposes `S` to hold `R/(2*A)` — the imaginary coefficient — and lines 103–104 print the conjugate pair in the form `a + b I` / `a - b I`.

### Key BASIC Idioms

- **SLOW/FAST switching:**`SLOW` is set at line 15 for readable I/O, `FAST` at line 47 for the arithmetic, then `SLOW` again at line 115 before the repeat prompt — a standard pattern to avoid flicker during calculation.
- **Input echo:** After each `INPUT`, the entered value is re-printed with leading spaces (e.g., line 35 `PRINT " ";A`), compensating for the lack of inline input display in some display modes.
- **Single-character string input:**`DIM A$(1)` at line 16 declares a one-character string for the yes/no response, avoiding wasted memory.
- **Variable reuse:**`S` is first used as the discriminant, then overwritten at line 102 with the imaginary coefficient — economical but potentially confusing if the program were extended.

### Notable Techniques

The `RUN` statement at line 135 (without a line number) restarts the entire program from the beginning, which reinitializes all variables. This is simpler than a `GO TO 10` loop but has the side effect of clearing all variables, including any that might be reused — in this program that is harmless since fresh coefficients are always requested.

### Bugs and Anomalies

- The boundary case `S = 0` (a repeated real root) is handled correctly by the real-root branch, and both printed values will be identical, which is mathematically accurate.
- The yes/no validation loop at lines 150–160 sends control back to line 120 to re-prompt, but does not prevent the user from entering multi-character strings — only the first character matters given `DIM A$(1)`.
- Lines 170–180 (`SAVE` followed by `GOTO 10`) are unreachable under normal execution, as no code path leads there. They appear to be a maintenance artifact left in the listing.
- The superscript “2” in the equation display is faked by printing `" 2"` on a separate line above `"WHERE AX +BX +C = 0"` (lines 30–31), a common workaround for the lack of superscript characters.

## Source Code

```
  10 CLS
  15 SLOW
  16 DIM A$(1)
  20 PRINT "ROOTS OF QUADRATIC EQUATIONS"
  25 PRINT 
  30 PRINT "        2"
  31 PRINT "WHERE AX  +BX +C = 0"
  32 PRINT 
  33 PRINT "ENTER COEFFICIENT A";
  34 INPUT A
  35 PRINT "  ";A
  36 IF A=0 THEN GOTO 33
  38 PRINT "ENTER COEFFICIENT B";
  39 INPUT B
  40 PRINT "  ";B
  41 PRINT "ENTER COEFFICIENT C";
  45 INPUT C
  46 PRINT "  ";C
  47 FAST
  50 LET S=B*B-4*A*C
  60 LET R=SQR (ABS S)
  70 IF S<0 THEN GOTO 100
  80 PRINT "THE ROOTS ARE REAL AND ARE:"
  85 PRINT (-B-R)/(2*A);" AND ";(R-B)/(2*A)
  90 GOTO 110
 100 PRINT "THE ROOTS ARE COMPLEX NUMBERS:"
 102 LET S=R/(2*A)
 103 PRINT "    ";-B/(2*A);" + ";S;" I"
 104 PRINT "AND ";-B/(2*A);" - ";S;" I"
 110 PRINT 
 115 SLOW
 120 PRINT "DO YOU WANT TO DO ANOTHER ONE?"
 130 INPUT A$
 135 IF A$="Y" THEN RUN 
 140 IF A$="N" THEN STOP
 150 PRINT "ENTER YES OR NO"
 160 GOTO 120
 170 SAVE "QUADRATI[C]"
 180 GOTO 10
```