The most accurate approximations of the roots of the quadratic equation 1 3 x 2 − 123 4 x + 1 6 = 0 , using four digit chopping arithmetic and to compute the absolute and relative errors.

Question

For context, the image provided below is a question from a September, 2024 past paper in statistical modeling

Answer 1

Question

Chapter 1.2, Problem 17ES

a.

To determine

The most accurate approximations of the roots of the quadratic equation 13x2−1234x+16=0, using four digit chopping arithmetic and to compute the absolute and relative errors.

b.

To determine

The most accurate approximations of the roots of the quadratic equation 13x2+1234x−16=0, using four digit chopping arithmetic and to compute the absolute and relative errors.

c.

To determine

The most accurate approximations of the roots of the quadratic equation 1.002x2−11.01x+0.01265=0, using four digit chopping arithmetic and to compute the absolute and relative errors.

d.

To determine

The most accurate approximations of the roots of the quadratic equation 1.002x2+11.01x+0.01265=0, using four digit chopping arithmetic and to compute the absolute and relative errors.

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For context, the image provided below is a question from a September, 2024 past paper in statistical modeling

If u use any type of chatgpt, will.downvote.

A function is defined on the interval (-π/2,π/2) by this multipart rule: if -π/2 < x < 0 f(x) = a if x=0 31-tan x +31-cot x if 0 < x < π/2 Here, a and b are constants. Find a and b so that the function f(x) is continuous at x=0. a= b= 3

Answer 2

Question

Chapter 1.2, Problem 17ES

a.

To determine

The most accurate approximations of the roots of the quadratic equation 13x2−1234x+16=0, using four digit chopping arithmetic and to compute the absolute and relative errors.

b.

To determine

The most accurate approximations of the roots of the quadratic equation 13x2+1234x−16=0, using four digit chopping arithmetic and to compute the absolute and relative errors.

c.

To determine

The most accurate approximations of the roots of the quadratic equation 1.002x2−11.01x+0.01265=0, using four digit chopping arithmetic and to compute the absolute and relative errors.

d.

To determine

The most accurate approximations of the roots of the quadratic equation 1.002x2+11.01x+0.01265=0, using four digit chopping arithmetic and to compute the absolute and relative errors.

Expert Solution & Answer

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Answer 3

Question

Chapter 1.2, Problem 17ES

a.

To determine

The most accurate approximations of the roots of the quadratic equation 13x2−1234x+16=0, using four digit chopping arithmetic and to compute the absolute and relative errors.

b.

To determine

The most accurate approximations of the roots of the quadratic equation 13x2+1234x−16=0, using four digit chopping arithmetic and to compute the absolute and relative errors.

c.

To determine

The most accurate approximations of the roots of the quadratic equation 1.002x2−11.01x+0.01265=0, using four digit chopping arithmetic and to compute the absolute and relative errors.

d.

To determine

The most accurate approximations of the roots of the quadratic equation 1.002x2+11.01x+0.01265=0, using four digit chopping arithmetic and to compute the absolute and relative errors.

Expert Solution & Answer

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Answer 4

Question

Chapter 1.2, Problem 17ES

a.

To determine

The most accurate approximations of the roots of the quadratic equation 13x2−1234x+16=0, using four digit chopping arithmetic and to compute the absolute and relative errors.

b.

To determine

The most accurate approximations of the roots of the quadratic equation 13x2+1234x−16=0, using four digit chopping arithmetic and to compute the absolute and relative errors.

c.

To determine

The most accurate approximations of the roots of the quadratic equation 1.002x2−11.01x+0.01265=0, using four digit chopping arithmetic and to compute the absolute and relative errors.

d.

To determine

The most accurate approximations of the roots of the quadratic equation 1.002x2+11.01x+0.01265=0, using four digit chopping arithmetic and to compute the absolute and relative errors.

Expert Solution & Answer

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Answer 5

Chapter 1.2, Problem 17ES

a.

To determine

The most accurate approximations of the roots of the quadratic equation 13x2−1234x+16=0, using four digit chopping arithmetic and to compute the absolute and relative errors.

b.

To determine

The most accurate approximations of the roots of the quadratic equation 13x2+1234x−16=0, using four digit chopping arithmetic and to compute the absolute and relative errors.

c.

To determine

The most accurate approximations of the roots of the quadratic equation 1.002x2−11.01x+0.01265=0, using four digit chopping arithmetic and to compute the absolute and relative errors.

d.

To determine

The most accurate approximations of the roots of the quadratic equation 1.002x2+11.01x+0.01265=0, using four digit chopping arithmetic and to compute the absolute and relative errors.

Answer 6

Chapter 1.2, Problem 17ES

a.

To determine

The most accurate approximations of the roots of the quadratic equation 13x2−1234x+16=0, using four digit chopping arithmetic and to compute the absolute and relative errors.

Answer 7

Chapter 1.2, Problem 17ES

a.

To determine

The most accurate approximations of the roots of the quadratic equation 13x2−1234x+16=0, using four digit chopping arithmetic and to compute the absolute and relative errors.

Answer 8

b.

To determine

The most accurate approximations of the roots of the quadratic equation 13x2+1234x−16=0, using four digit chopping arithmetic and to compute the absolute and relative errors.

Answer 9

b.

To determine

The most accurate approximations of the roots of the quadratic equation 13x2+1234x−16=0, using four digit chopping arithmetic and to compute the absolute and relative errors.

Answer 10

c.

To determine

The most accurate approximations of the roots of the quadratic equation 1.002x2−11.01x+0.01265=0, using four digit chopping arithmetic and to compute the absolute and relative errors.

Answer 11

c.

To determine

The most accurate approximations of the roots of the quadratic equation 1.002x2−11.01x+0.01265=0, using four digit chopping arithmetic and to compute the absolute and relative errors.

Answer 12

d.

To determine

The most accurate approximations of the roots of the quadratic equation 1.002x2+11.01x+0.01265=0, using four digit chopping arithmetic and to compute the absolute and relative errors.

Answer 13

d.

To determine

The most accurate approximations of the roots of the quadratic equation 1.002x2+11.01x+0.01265=0, using four digit chopping arithmetic and to compute the absolute and relative errors.

Answer 14

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Answer 15

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Answer 25

Ch. 1.1 - Show that the following equations have at least...Ch. 1.1 - Show that the following equations have at least...Ch. 1.1 - Find intervals containing solutions to the...Ch. 1.1 - Find intervals containing solutions to the...Ch. 1.1 - Find maxaxb |f(x)| for the following functions and...Ch. 1.1 - Find maxaxb | f(x)| for the following functions...Ch. 1.1 - Show that f(x) is 0 at least once in the given...Ch. 1.1 - Suppose f C[a, b] and f (x) exists on (a, b)....Ch. 1.1 - Let f(x) = x3. a. Find the second Taylor...Ch. 1.1 - Find the third Taylor polynomial P3(x) for the...

The most accurate approximations of the roots of the quadratic equation 1 3 x 2 − 123 4 x + 1 6 = 0 , using four digit chopping arithmetic and to compute the absolute and relative errors.

Solution Summary: The author calculates the absolute and relative errors of the given quadratic equation using four digit chopping arithmetic.

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The most accurate approximations of the roots of the quadratic equation 13x2−1234x+16=0, using four digit chopping arithmetic and to compute the absolute and relative errors.

The most accurate approximations of the roots of the quadratic equation 13x2+1234x−16=0, using four digit chopping arithmetic and to compute the absolute and relative errors.

The most accurate approximations of the roots of the quadratic equation 1.002x2−11.01x+0.01265=0, using four digit chopping arithmetic and to compute the absolute and relative errors.

The most accurate approximations of the roots of the quadratic equation 1.002x2+11.01x+0.01265=0, using four digit chopping arithmetic and to compute the absolute and relative errors.

Chapter 1 Solutions