Question

Mathematica is a program that allows the user to input complex math equations and get detailed answers. It uses the same style as WolframAplha

Use Mathematica to do the following problems.
1. Plot the polynomial function 2x^5-7x^3-5x^2+3x+1=0, and apply "FindRoot" to find each of its real roots.
2. A rectangular box has a surface area of 454 cm^2. Given that one face has an area of 80 cm^2 with a perimeter of 42 cm, find the dimensions of the box.
3. There are two discs with a combined circumference of 110 cm and a combined area of 550 cm^2. Find the radii of each disc.

Answer 1

Question 1:

First of all we input the given Polynomial. Then we plot the Polynomial

as in the plot of given Polynomial, we can observe that we have root in between -2 and 2 . So we will check in the neighborhood points i.e. -2,-1,1,2.

Hence we will put input FIndRoot for these points

So from the output , we have the desired real roots . And we have 3 real roots.

Root 1= -0.260628

Root 2=0.559125

Root 3=2.07381