Question

Coleman uses his graphing calculator to find all of the solutions to the equation shown below.

23 + 3 = -24 + 4
What are ALL of the solutions to the equation, rounded to the nearest hundredth?
A.
x = 0.82 and 3.55
B. O x = -1.38 and 0.37
C.
x = 0.37 and 3.55
D.Ox=-1.38 and 0.82

Answer 1

The correct option is;

D. x = -1.38 and 0.82

Please find attached the combined function chart

Explanation:

The given equation is x³ + 3 = -x⁴ + 4

Plotting the equation using Excel, we have;

f(x) = x³ + 3, h(x) = -x⁴ + 4

x f(x) h(x)

-1.4 0.256 0.1584

-1.39 0.314381 0.26699

-1.38 0.371928 0.373261

-1.37 0.428647 0.477246

-1.36 0.484544 0.57898

Which shows an intersection at the point around -1.38

x f(x) h(x)

0.77 3.456533 3.64847

0.78 3.474552 3.629849

0.79 3.493039 3.610499

0.8 3.512 3.5904

0.81 3.531441 3.569533

0.82 3.551368 3.547878

0.83 3.571787 3.525417

Which shows the intersection point around 0.82

Therefore, the correct option is x = -1.38 and 0.82

From the graphing calculator the intersection point is given as

x = -1.3802775691 and 0.81917251339.