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Chapter 3

Roots without solving

A polynomial's coefficients already know the sum and product of its roots.

1

Two roots

Drag the roots a and b. Watch what the coefficients of (x − a)(x − b) do.

-5-4-3-2-112345ab
(x−1)(x−4)(x - 1)(x - 4)==x2x^{2}− 5x-\,5x+ 4+\,4

a+b=5a + b = 5 · ab=4ab = 4

Next chapter: Same degree everywhere →