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Consider the function y=x^3 - 2x^2 + k, where k is a constant. Explain why k=0 ensures that f(x)=0 has a double root. A double root is a bounce and I thought that when k=0, the x^2 can be immediately common factored out of the function, so you have (x^2)(x-2)=0. Therefore, you will always have a bounce with that x^2. Am I even close?
Also, I have to determine another value of k that ensures f(x)=0 has a double root. This I am completely stuck on...
Also, I have to determine another value of k that ensures f(x)=0 has a double root. This I am completely stuck on...