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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 at the Kumar and we'll start with very simple examples. The question here is that the height of a box with a

square

base is 4 centimeters more than the length of the side of its

square

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

dimensions

? So first let's draw a

square

base box so we'll have a higher height so we'll have a taller box like this and the

square

means something like the top right so let's make this box like this so that it's the box be X the length of the base and XP the height of the wave is 4 moves so our height will be X plus 4 this is how we can define our variables so we have the length and width of X and the height of X plus 4 the volume in terms of X can be written as a function V of x equals 2x times X times X plus 4 wedges we can open these brackets X cubed plus 4 X

square

d so that's the volume of For this box you can say that X

square

d is the area of ​​the base multiplied by the height X cubed plus 4 X

square

d either way if the volume of the box is 225 cubed centimeters what are its

dimensions

then the volume is 225 minus replaced V of X is 225 and then we have that it must be equal to X cubed plus 4x

square

d we need to

find

the value of x so subtract 225 from both sides we get 0 equals 2x cubed plus 4x

square

d minus 225 Now to

find

the zeros for this

polynomial

we must drive, which are factors of 225.
solve polynomial equation to find dimensions of square based box
Now, a good value to test is five, so let's call this a

polynomial

, so for this

polynomial

, test the value of five, so you can take your calculator and then calculate 5q plus four times five

square

d minus 225 is equal to which gives us five cubes plus four times five

square

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

find

the rest of the factors, we can do synthetic division and

find

the

equation

so that we at least have a value of x and that gives us that x is equal to five can give a set of solutions if I substitute X is 5 then I get length and width is 5 and the height will be 5 plus 4 which is 9 units are cent imeter so b Well, the question is almost complete at this stage, we can also write our answer and our answer is that the

dimensions

are 5 centimeters by 5 centimeters by 9 centimeters, so that's the dimension of the box, but there's no harm in continuing from OK 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 is that the coefficients are 1, that's 4x cubed x

square

d, that's 4, let's substitute 0 times X and we have minus 225 3 5 is a factor I should say that X minus 5 is a factor so we can divide by 5 What do we get?
solve polynomial equation to find dimensions of square based box
Reduce 1 multiply by five to get five five plus four is nine five times nine is forty five we add forty five times five to twenty five, so we get zero as expected, which means that the

polynomial

hour can be written as so that we can write the

polynomial

function as equal to I refer to this point in my question as X minus five times that's

square

d plus 9x plus forty five according to

equation

now c and

find

if there are any more solutions to this ok that means more factors of this quadratic

equation

now if you try to

solve

this quadratic

equation

then what you get let's use the quadratic

equation

since x equals two minus P which is negative 9 plus or minus B The

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 we get a negative term here divided by 2 which means there are no more solutions that are not real correct so the only combination n is what we have and now we can write our too sure the

dimensions

are five centimeters by two centimeters by three centimeters well some of you might think at the stage that it was kind of a waste of time to try the other routes you will soon

find

questions in the test where the wording will be different they say what are the possible

dimensions

what are all the possible

dimensions

and in some of those cases you can

find

some real roots and different combinations of solutions so the idea of ​​taking this is even if you got an answer please try to see others you have such simple quality

equation

s to

solve

and there is a chance of getting more than one solution so go ahead that is my advice at this stage and now let's move on to the next question hope you appreciate it thanks and all the best
solve polynomial equation to find dimensions of square based box
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