Question

Write the polynomial of least degree with roots -2, 0, 1.

Answer 1

So since -2, 0, 1 are the roots:

Therefore  x = -2,  x = 0 ,  x = 1

Implies that:

x = 2        x - 2 = 0

x = 0          x = 0

x = 1        x - 1 = 0


Therefore    (x - 2)x(x - 1) = 0

(x - 2)(x - 1) =   x(x - 1) - 2(x - 1) =  x² - x - 2x + 2 = x² - 3x + 2

(x - 2)x(x - 1) = 0

(x - 2)(x - 1)x = 0

(x² - 3x + 2)x = 0

x*x² - x*3x + x*2 = 0

x³ - 3x² + 2x = 0

This is the polynomial with the least degree, because it possible for another polynomial with higher power to still have the same root.

 x³ - 3x² + 2x = 0    is the polynomial.

I hope this helps.