antbanks3050
02.04.2020 •
Mathematics
Let $3x^2 + 4x + c = 0.$ What value of $c$ will give us exactly one solution for $x$?
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Ответ:
If y = ax + 2a², then its derivative is dy/dx = a. Substitute y and dy/dx into the given equation and check if it results in an identity:
2 (dy/dx)² + x dy/dx - y = 0
2a² + ax - (ax + 2a²) = 0
0 = 0
This is of course true, so y = ax + 2a² is indeed a solution to the given equation.