The equation has roots .
Find the equation with roots
For this I so far have:
= -4
= 3
= -2
How would I progress from here?
Right, I found an answer for this question in detail now but I'm now sure how this works either:
It says consider = 3
then
= -2 multiplied by -4 = 8
How does the equation with the squares originate? What do you calculate in order to get to that?
There was asked for an equation with roots .
is ofcourse such an equation.
If you multiply all the factors you see the result is what I've written out.
the last coefficient is
I have multiplied that out but it doesn't make anything easier or make absolutely any sense to me!
My mark scheme says:
= -4
= 3
= -2
then consider = 3 [I understand this all up to here]
= -2 multiplied by -4 = 8 [I do not know how this works - where is the above line coming from?]
=
= 4 [I understand this]
then the required equation is
[I can see how it got here considering the previous working]
All I really want to know is how the mark scheme has come to this! I understand most of it, barring the line which results in "=8".
Then I wonder how you came to these relations
The only way you could have found these relations is by considering
Then the relations you start out with follow.
After that you want an equation with roots
An equation that satisfies this property is:
But we like to know explicitly how this polynomial looks like from the relations we derived.
Thus we write out this factored form: This can be tenacious work but it's not that hard actually. Mathematics is 10 % inspiration, 90% perspiration.
I came to the relations that you quoted by using: -b/a to get -4, c/a to get 3 and -d/a to get -2 which was simple enough.
I agree with what you said about mathematics, except with me much of the 90% perspiration is lost in confusion.
Please could you write out a solution? I have tortured myself too long over this question and have tried what you said - expanding those brackets but I can't do that without obtaining and in a number of terms and it doesn't add up to what my mark scheme details.