whats a double root?

Question

eg. Solve the equation, noting any double roots: x^3+9x=6x^2

Answer 1

A double root is something that has a square factor, like x^2=0 which has x=0 as a "double" root.

For this equation subtract to get x^3-6x^2+9x=0 then factor out the x: x(x^2-6x+9)=0 then factor more to get x(x-3)(x-3)=0 so x=0 is one solution and x=3 is another solution and x=3 is a double root [two factors of (x-3)]

Answer 2

Double Root

Answer 3

To explain what a double root is, I'll first solve your equation.

x^3 + 9x = 6x^2

x^3 - 6x^2 + 9x = 0
x(x^2 - 6x + 9) = 0
x(x - 3)(x - 3) = 0

Therefore, x = {0, 3, 3}

The Fundamental Theorem of Algebra states that ANY polynomial equation of degree n has exactly n roots (including multiplicity). It seems a bit abnormal to say that the solutions are x = {0, 3, 3} when it makes more sense to say x = {0, 3}. The fact that there is another hidden "3" that results from the way the polynomial factors is why it is a double root; because there are 2 of them in all.

Answer 4

A double root Double is a root of a polynomial equation with multiplicity 2. Also refers to a zero of a polynomial function with multiplicity 2.

Guido