Find every root of a quadratic, cubic or quartic in one step - including roots that don’t factorise nicely.
In short: A polynomial solver finds every root of an equation such as a cubic or quartic once you enter its coefficients, including complex roots on models that support them. It is much faster than factorising by hand. Read off the real roots when the question asks for real solutions, and give answers to the accuracy requested.
| TI-84 Plus CE | Casio fx-CG50 and fx-CG100 | TI-Nspire CX | |
|---|---|---|---|
| Key sequence | Use the PlySmlt2 app: APPS → PlySmlt2 → Polynomial Root Finder. Set the degree, enter the coefficients, then SOLVE. | Main menu → Equation → Polynomial, choose the degree, enter the coefficients, then SOLVE. | menu → Algebra → Polynomial Tools → Find Roots of a Polynomial, or type polyRoots(expr, x). |
Tip: Set the degree to match the highest power. Complex roots show as a ± bi on models that support them; real roots are where the graph crosses the x-axis.
Tip: Set the degree to match the highest power. Complex roots show as a ± bi on models that support them; real roots are where the graph crosses the x-axis.
Tip: Set the degree to match the highest power. Complex roots show as a ± bi on models that support them; real roots are where the graph crosses the x-axis.
Here's a real IB-style question that uses exactly this technique.
Find all real roots of 2x³ − 3x² − 11x + 6 = 0.
Find every root of a quadratic, cubic or quartic in one step - including roots that don’t factorise nicely. A cubic or quartic doesn't factorise nicely, so the usual by-hand methods don't work cleanly. A question asks for all real roots of a polynomial, including ones that aren't whole numbers.
1. Write the polynomial in standard form, e.g. 2x^3 − 3x^2 − 11x + 6 = 0. 2. Use the PlySmlt2 app: APPS → PlySmlt2 → Polynomial Root Finder. Set the degree, enter the coefficients, then SOLVE.
1. Write the polynomial in standard form, e.g. 2x^3 − 3x^2 − 11x + 6 = 0. 2. Main menu → Equation → Polynomial, choose the degree, enter the coefficients, then SOLVE.
1. Write the polynomial in standard form, e.g. 2x^3 − 3x^2 − 11x + 6 = 0. 2. menu → Algebra → Polynomial Tools → Find Roots of a Polynomial, or type polyRoots(expr, x).
Set the degree to match the highest power. Complex roots show as a ± bi on models that support them; real roots are where the graph crosses the x-axis.
In the worked example on this page (3 marks, Paper 2), the marks are: M1: Set up the polynomial root finder with coefficients 2, −3, −11, 6; A1: x = −2, x = 1/2, x = 3 (all three roots).
Questions that need this technique link back to this guide. Try one in practice mode, or see every GDC guide.