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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

Sagot :

xero099

Answer:

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

Step-by-step explanation:

Let [tex]f(x) = -x^{3}+2\cdot x^{2} + 3\cdot x[/tex], to determine its roots and multiplicities we proceed to factorize the polynomial:

1) [tex]-x^{3}+2\cdot x^{2} +3\cdot x[/tex] Given

2) [tex]x\cdot (-x^{2}+2\cdot x + 3)[/tex] Distributive property

3) [tex]x\cdot (x-3)\cdot (x+1)[/tex] Quadratic formula/Result

The roots and multiplicities of [tex]f(x) = -x^{3}+2\cdot x^{2} + 3\cdot x[/tex] are:

0 (multiplicity 1)

3 (multiplicity 1)

-1 (multiplicity 1)

Therefore, the correct answer is A.

Answer:

The answer would be A!

Step-by-step explanation:

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

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