Dawnbridge

TI-Nspire CX II field manual for IB Math

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14

Finding roots of a polynomial

All courses

Use the calculator's polynomial root finder to enter the coefficients of a polynomial and read all real roots.

Goal

Find the real roots of ​x3−7x+6=0.

1

From the Scratchpad calculator, open the polynomial root command: press → 3: Algebra → 3: Polynomial Tools → 1: Find Roots of Polynomial.

2

Choose degree 3. Enter the coefficients in descending powers of ​x, moving between the boxes with : 1, 0, -7, 6. The ​x2​ coefficient is ​0, so include that zero in the list. Use for the negative sign in -7.

Scratchpad
RAD
Roots of a Polynomial
Degree3▶
Real or ComplexReal▶
OKCancel
3

Press to solve. The Nspire returns the roots as a list.

Scratchpad
RAD
polyRoots({1.,0.,−7.,6.},x)
{−3.,1.,2.}
Result

The roots are ​x=−3,  ​x=1, and ​x=2.

Your turn

Work each one on your calculator, then check the answer.

  1. 1

    Find all real roots of ​x3−13x+12=0.

  2. 2

    Find all real roots of ​x3−19x+30=0.

  3. 3

    Find all real roots of ​x3−21x−20=0.