The equation has roots .
Find the equation with roots
For this I so far have:
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
= -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
My mark scheme says:
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
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 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.