SOLUTION: If one zero of the function y= x^2 + mx + n is the square of the other, without finding the zeroes, prove that m^3 = n(3m - n - 1). Thanks in advance. P.S: Is there a method

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: If one zero of the function y= x^2 + mx + n is the square of the other, without finding the zeroes, prove that m^3 = n(3m - n - 1). Thanks in advance. P.S: Is there a method       Log On


   

Question 625084: If one zero of the function y= x^2 + mx + n is the square of the other, without finding the zeroes, prove that m^3 = n(3m - n - 1).
Thanks in advance.
P.S: Is there a method of proving without substitution involved?
Answer by oscargut(2103) About Me  (Show Source):
You can put this solution on YOUR website!
Nice problem !!
Here is my answer
y= x^2 + mx + n
Zeros are: a and a^2
Sum of the zeros = -m
a+a^2 = -m
a(a+1) = -m (equation 1)
product of the zeros = n
a^3 = n (equation 2)

From eq 1)and 2)
(-m)^3 = a^3(a+1)^3 = n(a^3+3a^2+3a+1) = n(n-3m+1)
Then: -m^3 = n(n-3m+1)
m^3 = n(3m-n-1)


If you have any doubt or if you have more problems my e-mail is:
mthman@gmail.com