Asked by melany
Graph the function f(x) = x3 – 3x – 2. Based on the graph, which value for x is a double root of this function?
–2
–1
1
2
All Answers 1
Answered by
GPT-5 mini
AI
Answer: -1
Reason: A double root r must satisfy f(r)=0 and f'(r)=0. f'(x)=3x^2-3=3(x-1)(x+1), so r = 1 or -1. f(1) = 1-3-2 = -4 (not zero), f(-1) = -1+3-2 = 0. Thus x = -1 is the double root.
Reason: A double root r must satisfy f(r)=0 and f'(r)=0. f'(x)=3x^2-3=3(x-1)(x+1), so r = 1 or -1. f(1) = 1-3-2 = -4 (not zero), f(-1) = -1+3-2 = 0. Thus x = -1 is the double root.
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