If f(x)=2x^4-3x^3+2x^2+x-3, explain how you know that the equation f(x)=0 has at least one real root between x=1 and x=2
1 answer:
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Answer:
B. x ≈ 13/8
Step-by-step explanation:
We assume that one iteration consists of determining the midpoint of the interval known to contain the root.
The graph shows the functions intersect between x=1 and x=2, hence our first guess is x = 3/2.
Evaluation of the difference between the left side expression and the right side expression for x = 3/2 shows that difference to be negative, so we can narrow the interval to (3/2, 2). Our 2nd guess is the midpoint of this interval, so is x = 7/4.
Evaluation of the difference between the left side expression and the right side expression for x = 3/4 shows that difference to be positive, so we can narrow the interval to (3/2, 7/4). Our 3rd guess is the midpoint of this interval, so is x = 13/8.
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The sign of the difference at this value of x is still negative, so the next guess would be 27/16. It is a little hard to tell what the question means by "3 iterations." Evaluating the function for x=13/8 will be the third evaluation, so the determination that x=27/16 will be the next guess might be considered to be the result of the 3rd iteration.
