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)…

Question

asked Apr 14, 2019 235k views

2 Answers

Csjpeter · Answer 1 · 2019-04-16T07:31:36+0000

Answer: Option 'A' is correct.

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.

Szimek · Answer 2 · 2019-04-18T15:10:47+0000

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.