The roots of the equations #x^3+ax^2+bx+c=0# are three consecutive integers. Find all possible values of #a^2/(b+1)#?
I have no idea how to get there. Please include steps and explanations!
I have no idea how to get there. Please include steps and explanations!
1 Answer
Explanation:
We know that the product of the factors for the 3 roots is equal to the polynomial:
Because we are told that the roots are consecutive integers, we can rewrite the above in terms of the lowest root:
Distribute the minus signs:
Here is the results of the multiplication:
Matching coefficients with
Compute
Compute
Divide equation [2] by equation [1]:
The quadratics cancel to show that the value of