Question

ANSWER FOR 25 POINTS!!!

Answer 1

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

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  $x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12.$

Answer: correct choice is A.

Answer 2

Answer: Option 'A' is correct.

Step-by-step explanation:

Since we have given that

Systems of two equations :

$x^3 - 2x^2 + 5x - 6\ and-4x^2 + 14x + 12$

And according to question, we have

$x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12$

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

$x=-3,x=-2,x=3$

and if simplify the above equations, we get,

$x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12\\\\x^3-2x^2+5x-6+4x^2-14x-12=0\\\\p(x)=x^3+2x^2-9x-18$

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

$p(-3)=-27+18+27-18=0\\\\p(-2)=-8+8+18-18=0\\\\p(3)=27+18-27-18=0$

$-3,-2\ and\ 3\text{ are the roots of the polynomial equation}$

Hence, Option 'A' is correct.