Eli Whitney invented the the cotten gin
2 answers:
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You haven't provided the required roots, but I can tell you how to do this kind of exercises in general.
If the coefficient is 1, i.e. the equation is written like
, then you can say the following about the coefficients b and c:
is the opposite of the sum of the roots
is the multiplication of the roots.
So, for example, if we want an equation whose roots are 4 and -2, we have:
So, the equation is
If your roots are rational, you can work like this: suppose you want an equation with roots 3/4 and 1/2. You have:
And so the equation is
In order to have integer coefficients, you can multiply both sides of the equation by 8: