SOLUTION: Prove that the roots of 2𝑥 2 + (1 − 2𝑛)𝑥 − 𝑛 = 0 are rational and unequal if 𝑛 is an integer.

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Question 1178991: Prove that the roots of 2𝑥
2 + (1 − 2𝑛)𝑥 − 𝑛 = 0 are rational and
unequal if 𝑛 is an integer.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!

2𝑥^2 + (1 − 2𝑛)𝑥 − 𝑛 = 0
comparing the equation with ax^2 +bx +c
a= 2, b=(1-2n), c=-n
b^2 = (1-2n)^2
1-4n +4n^2
4ac = (4)(2)(-n)
= -8n
b^2 -4ac
1-4n +4n^2 -(-8n)
4n^2 -3n +1
4n^2+4n+1
(2n+1)^2
For all values of n, (2n+1)^2 >0
Therefore roots are real and unequal