Two equal roots occur at a place where the function has a slope of zero.
The derivative of the given function is 3*x^2 + 6*x  9. Its zeros are x=3 and 1.
At x=3, c would need to be 27 to make the function zero at that point of zero slope.
At x = 1, c needs to be 5 to bring the function to zero when its derivative is zero.
As c needs to be positive, the answer is 5.

Posted by Charlie
on 20240212 12:57:56 