SOLUTION: Find the values of m for which the quadratic curve y = 3mx^2 + 2mx + 1 touches the x axis exactly once .

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Question 1051371: Find the values of m for which the quadratic curve y = 3mx^2 + 2mx + 1 touches the x axis exactly once .
Answer by ikleyn(52781) About Me  (Show Source):
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Answer. m = 3.

Solution 

A necessary and sufficient condition is  3mx%5E2+%2B+2mx+%2B+1 = %28ax%2Bb%29%5E2.


Comparing coefficients, it gives b = 1,  a = m,  a%5E2 = 3m,

which implies  m%5E2 = 3m  --->  m = 3.


Another solution m = 0 doesn't suit the condition.