SOLUTION: Forwhat value of k, the expression k2x2 + 2(k + 1) x + 4 is perfect
square
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Question 1020032: Forwhat value of k, the expression k2x2 + 2(k + 1) x + 4 is perfect
square
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
x\ +\ 4\ =\ 0)
}{k^2}x\ +\ \frac{4}{k^2})
Which is a perfect square iff:
}{2(k^2)}x\right)^2\ =\ \frac{4}{k^2})
Leaving the intermediate steps as an exercise for the reader, we have:
Which factors to:
(3k\ +\ 1)\ =\ 0)
Hence
or
Check:
x\ +\ 4\ =\ 0)
^2)
Or
^2x^2\ +\ 2\left(-\frac{1}{3}\ +\ 1\right)\ +\ 4\ =\ 0)
x^2\ +\ \frac{4}{3}x\ + 4\ =\ 0)
^2)
John
My calculator said it, I believe it, that settles it
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