Problems Involving Polynomial Equation and its Roots

Question 1

John made a box that can contain 200 cm^3 of sand. If the length of the box is twice its width and the height is 1 cm shorter than its width.
Can you give possible combinations for the length, width and height of the box?

Answer 1

l = 2x
w = x
h = x-1

Question 2

SOLVE THE PROBLEM
John made a box that can contain 200 cm^3 of sand. If the length of the box is twice its width and the height is 1 cm shorter than its width.

Answer 2

x = 5 cm
l = 10 cm
w = 5 cm
h = 4 cm

Question 3

Determine whether this given numbers (7, -3 and 9) are roots of the polynomial equation x^3+x^2-6x-756

Answer 3

7 NO
-3 NO
9 YES

Question 4

A 3ft ladder leans against a wall and the distance from the top of the ladder to the ground is 7ft more than the distance from the bottom of the ladder to the wall. What is the distance from the top of the ladder to the ground?

Answer 4

12 ft

Question 5

The length of a rectangular window is 4ft more than its width. If the area is 60ft^2, what are the dimensions of the window?

Answer 5

6 ft and 10 ft