2 final questions: max. area w/ given perim.; roots of cubic

[mxrider477]

I need help with these 2 final questions in my math class. Will someone please help!

1) Find the dimensions of a rectangle A with the greatest area whose perimeter is 30 feet.

2) Given x^3 - 4x^2 + 2x + 1 = 0, how many possible negative roots are there?
Find the irrational roots of the equation. (Hint: Use the quadratic formula to solve the depressed equation.)

I would greatly appricate any and all help. Thanks.

 

[stapel]

1) Draw the rectangle. Label the length and width with variables of your choice. Plug these into the formula for the perimeter of a rectangle, using the given value of the perimeter to complete the equation.

Solve the equation for one of the variables (your choice).

Write the formula for the area of a rectangle. Use the result of the last step to substitute for one of the variables. This gives you the area in terms of only one variable.

The area equation is now a quadratic function, "A = (a quadratic in one variable)". Find the vertex.

2) If I recall the name correctly, you're supposed to apply Descartes' Rule of Signs to find the number of positive or negative roots.

Use the Rational Roots Test and synthetic division (and maybe a graph on your calculator) to find one (rational) root. Then use the Quadratic Formula to find the remaining roots.

If you get stuck, please reply showing how far you have gotten in following the instructions. Thank you.

Eliz.