Question

What is the multiple zero and multiplicity of f(x)=x^3+2x^2+x? Help needed !!

A. Multiple zero =-1; multiplicity = 2

B. Multiple zero =1;multiplicity =2

C. Multiple zero = 2; multiplicity =-1

D. Multiple zero =2; multiplicity =1

Answer 1

A

Explanation:

Answer 2

f(x) = x³ + 2x² + x

f(x) = x.(x² + 2x + 1)

f(x) = x.(x + 1)²

So, f(x) = 0 when x = 0 or when x = -1

But

f(x) = x.(x + 1)² = x.(x + 1).(x + 1)

So we have three roots, x = 0, x = -1 and x = -1, although two of them are equal.

So we have a multiple zero x = -1 with a multiplicity 2.

Alterativa A.