What are the roots of the polynomial equation x^3-7x=6x-12? use a graphing calculator and a system of equations.
a .–6, 6
b. –4, 1, 3
c. –3, –1, 4
d. 1, 3

The roots are x = -4, 1 and 3.

B is the correct option.

Step-by-step explanation:

We have to find the roots of the polynomial

We can find the roots by forming a system of equations and with the help of a graphing calculator.

The system of equations for the given polynomial:

Now, we graph these equations in the xy-plane. The x-coordinate (s) of the intersection point will be the roots of the equation.

The graph is shown in the attached file.

The intersection points are (-4,-36),(1,-6) and (3,6). The x-coordinates are x = -4,1 and 3.

Therefore, the roots are x = -4, 1 and 3.

B is the correct option.

complete the steps to find the area of the trapezoid.

area of rectangle = 256   square units

area of triangle 1 = 24  square units

area of triangle 2 = 16  square units

area of triangle 3 =   96 square units

area of trapezoid = 120  square units

step-by-step explanation:

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.