Degree = Number of Roots
Every polynomial of degree has exactly roots.
Given the polynomial:
Tap to spawn exactly all its roots
Exact match!
Rational Root Theorem
Potential rational roots are factors of the constant () divided by factors of the leading coefficient ().
Factors of Constant ()
Drag here
Factors of Leading Coeff ()
Drag here
Drag the factors to the correct boxes
All tiles placed
Factors sorted!
Find the Actual Roots
Test the possible rational roots. If , you found a root!
Evaluating f()...
Awaiting input...
Tap to test numbers (Find 3)
All 3 roots found!
Complex Conjugate Theorem
If is a root, then must also be a root.
A polynomial has a root at:
Set the missing conjugate root
Real Part
{{ s4.userReal }}
Imaginary Part
{{ Math.abs(s4.userImag) }}i
Perfect match!
Theorem Mastered!
You've successfully explored the Fundamental Theorem of Algebra, finding roots using degrees, the Rational Root Theorem, direct testing, and complex conjugates!