Polynomials (1 Viewer)

[Lukybear]

I gota question on polynomials which i am stuck on.

A box is to have a square base and a height that is 10 cm longer than the length of the base. If the volume of the box is to be 2000cm^3, find the dimensions of the box.

So far ive got:
(x^3+10x^2-2000)/(x-10)=x^2+20x+200

this is where i get stuck...
there is no value for x in x^2+20x+200 as "b^2-4ac" is negative...

I know the answer is 10 10 20 but how would it be deduced?

 

[Finx]

Are you sure this is polynomials, because I've never seen a question quite like that =/

 

[Timothy.Siu]

I gota question on polynomials which i am stuck on.

A box is to have a square base and a height that is 10 cm longer than the length of the base. If the volume of the box is to be 2000cm^3, find the dimensions of the box.

So far ive got:
(x^3+10x^2-2000)/(x-10)=x^2+20x+200

this is where i get stuck...
there is no value for x in x^2+20x+200 as "b^2-4ac" is negative...

I know the answer is 10 10 20 but how would it be deduced?

u get x^3+10x^2-2000=0
(x-10)(x^2+20x+200)=0
as u said, theres no solution for the right part,
therefore x=10.
dimensions, 10,10,20

 

[Trebla]

Let the side of the base be x.
x²(x + 10) = 2000
x³ + 10x² - 2000 = 0
x³ - 1000 + 10x² - 1000 = 0
(x - 10)(x² + 10x + 100) + 10(x² - 100) = 0 (alternatively you could guess and check x = 10)
(x - 10)(x² + 10x + 100) + 10(x - 10)(x + 10) = 0
(x - 10)(x² + 10x + 100 + 10(x + 10)) = 0
(x - 10)(x² + 20x + 200) = 0
Since x² + 20x + 200 has no zeroes, then x = 10
Hence dimensions are 10cm, 10cm and 20cm.

 

[Lukybear]

O i c... so only the first factor is needed rite? Cause i thought if you factor the quadratic then you would get the other two answers.. guess i was wrong

thxs anywaz

 

[Timothy.Siu]

O i c... so only the first factor is needed rite? Cause i thought if you factor the quadratic then you would get the other two answers.. guess i was wrong

thxs anywaz

yeah, but this case has no other answers..sometimes there will be