Question

What is the multiplicity of each of the roots of the graph of f(x)=−-x^3+2x^2+3x?

A. -1, multiplicity 1; 0 multiplicity 1; 3 multiplicity 1
B. -1, multiplicity 3; 0 multiplicity 1; 3 multiplicity 1
C. -3, multiplicity 1; 0 multiplicity 1; 1 multiplicity 1
D. -1, multiplicity 1; 3 multiplicity 1

Answer 1

The answer would be A!

Explanation:

I did the question in class today. I hope this helped!

Answer 2

A. -1, multiplicity 1; 0, multiplicity 1; 3, multiplicity 1.

Explanation:

Let
`f(x) = -x^(3)+2\cdot x^(2) + 3\cdot x`, to determine its roots and multiplicities we proceed to factorize the polynomial:

1)
`-x^(3)+2\cdot x^(2) +3\cdot x` Given

2)
`x\cdot (-x^(2)+2\cdot x + 3)` Distributive property

3)
`x\cdot (x-3)\cdot (x+1)` Quadratic formula/Result

The roots and multiplicities of
`f(x) = -x^(3)+2\cdot x^(2) + 3\cdot x` are:

0 (multiplicity 1)

3 (multiplicity 1)

-1 (multiplicity 1)

Therefore, the correct answer is A.