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Solve Polynomial Equation to Find Dimensions of Square Based Box

Aug 23, 2022

Solve Polynomial Equation to Find Dimensions of Square Based Box

Polynomial

Equation

s I'm on the Kumar and we'll start with very simple examples. The question here is that the height of a

square

box is 4 centimeters greater than the side length of its

square

base if the volume of the box is 225 centimeters Cube what are its

dimensions

so let's sketch a

square

box first so we can make a taller one have height so we have taller box like this and

square

means something like top right so we make this box like this so is the box let X be the length of the base and XP the wave height is 4 moves so is ours Height X plus 4 so we can define our variables so we have length and width of X and height of X plus 4 Volume with respect to X can be written as a function V of x is equal to 2x times X times X plus 4 wedges .
solve polynomial equation to find dimensions of square based box
We can open these brackets X to the power of three plus 4 X

square

so the volume of this box is and you can say that X

square

is the area of ​​the base multiplied by the height of X to the power of three plus 4 X

square

in either direction if that Volume of the box 225 centimeters is cube, what are its

dimensions

, so the volume is 225 less, replacing V by X is 225, and then we have that it should be equal to X to the power of three plus 4 x

square

d. We need to

find

the value of x so we take away 225 from both sides we get 0 equals 2x cube plus 4x

square

minus 225 Now to

find

the zeros for this

polynomial

we should drive what are factors of 225.
solve polynomial equation to find dimensions of square based box
A good value to try is five so let's call this a

polynomial

so for this

polynomial

try the value five so let's try you can take a calculator and then calculate that 5q plus four times five

square

d minus 225 equals which gives us five cubic plus four times five

square

d minus 225 which is zero so we get a zero which means X minus five is a correct factor to

find

the rest of the factors we can actually do a synthetic division and

find

the

equation

such that we have at least one value of x and that gives us x equals five can give a range of solutions if i replace x with 5 then i get longitude and latitude is 5 and the height is 5 plus 4 which is 9 units cents well the question is almost complete at this point we can also write down our answer and our answer is that the

dimensions

5cm x 5cm x 9cm s ind, so the correct size of the box, but there's no harm in continuing here, since we know that one of the factors is 5, we can do synthetic division or long division, and here we have our

equation

, which are the coefficients 1 that's 4x cubic x

square

it's 4 let's substitute 0 for X and we have minus 225 3 5 is a factor I should say X minus 5 is a factor so we can divide by 5 what do we get 1 take down multiply by five so we get five five plus four is nine five times nine is forty five add forty five times five to twenty five so we actually get zero as expected which means the

polynomial

hora can be written as so we can use the

polynomial

function can be written as equal.
solve polynomial equation to find dimensions of square based box
I mean this point of my question correctly as X minus five times that is

square

plus 9x plus forty five by

equation

now we c

find

out if there are more solutions to this okay which means more factors of this quadratic

equation

. Now when you try to

solve

this quadratic

equation

we use the quadratic

equation

as x equals two minus P which is minus 9 plus or minus B

square

which is 9

square

d is 81 minus 4 times AC 4 times 45 is 4 times 5 is 20 4 times 4 is 16 and 2 is 180 so here we get a negative term divided by 2 which means there are no more solutions that aren't actually correct so the only combination is the one we get and now we can write ours with certainty that the

dimensions

are two inches by two inches by three inches.
solve polynomial equation to find dimensions of square based box
Well, some of you at the stage may think that this was kind of a waste of time trying the other routes soon you will come across questions in the test where the wording is different. They say what possible

dimensions

are, what all possible

dimensions

are. In some of these cases you might

find

some real roots and different combinations of solutions, so the idea to take this is even if you got an answer. Try to see the others. You have a quality

equation

that's so easy to keep solving and there's a chance you'll get more than one solution, so move on to the next question.
solve polynomial equation to find dimensions of square based box
I hope you appreciate it. Thank you very much and good luck
solve polynomial equation to find dimensions of square based box
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