Book Maths Puzzle Algebra

Part question on quadratic equations in intermediate algebra:

A quadratic equation can have zero, one or two solutions (zeroes) in the study of quadratic formulas and the discriminant.

1. What about an equation of order 3 like: ax^3+bx^2+cx+d=0

2. What is the minimum number of solutions or zeroes? What is the maximum? Can there be two?

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Book Other Question

Question regarding quadratic equations in intermediate algebra:

Determine the dimensions of a rectangle with a perimeter of 20 that encloses the greatest area. The perimeter is I have no clue how to do this. I am working on quadratic functions and their graphs in intermediate algebra. This is one question with three parts:

A. Write the function y=3(x-2)^2+6 in the form of Y=ax^2 +bx+c, and find the vertex of the parabola using the formula x=-b/2a

B. Repeat part (a) with the functions y=-4((x-5)^2-9 and y=3(x+2)^2-6.

C. What is the vertex for a parabola that is written in the form y=a(x-h)^2+k?