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

Answer:

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

Step-by-step 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.

Answer 2

Answer:

The answer would be A!

Step-by-step explanation:

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