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ANSWER FOR 25 POINTS!!!

Carlos graphed the system of equations that can be used to solve x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12

What are the roots of the polynomial equation?

A) –3, –2, 3

B) –3, 2

C) 18, 32

D) 18, 32, 66

ANSWER FOR 25 POINTS Carlos graphed the system of equations that can be used to solve x3 2x2 5x 6 4x2 14x 12 What are the roots of the polynomial equation A 3 2 class=

Respuesta :

frika

Carlos graphed two graphs: [tex]y=x^3 - 2x^2 + 5x - 6[/tex] and [tex]y=-4x^2 + 14x + 12.[/tex]

As you can see from the diagram, these two curves have three common points at x=-3, x=-2 and x=3.

These three points ae solutions of the equation  [tex]x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12.[/tex]

Answer: correct choice is A.

Answer: Option 'A' is correct.

Step-by-step explanation:

Since we have given that

Systems of two equations :

[tex]x^3 - 2x^2 + 5x - 6\ and-4x^2 + 14x + 12[/tex]

And according to question, we have

[tex]x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12[/tex]

We can see from the graph that "The two equations are intersected at "

[tex]x=-3,x=-2,x=3[/tex]

and if simplify the above equations, we get,

[tex]x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12\\\\x^3-2x^2+5x-6+4x^2-14x-12=0\\\\p(x)=x^3+2x^2-9x-18[/tex]

But the roots will be same as above as they both get intersected at these points only,and

[tex]p(-3)=-27+18+27-18=0\\\\p(-2)=-8+8+18-18=0\\\\p(3)=27+18-27-18=0[/tex]

[tex]-3,-2\ and\ 3\text{ are the roots of the polynomial equation}[/tex]

Hence, Option 'A' is correct.

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